In equation (17.2), the first term describes a deterministic process - trend, and the second - stochastic process. In Fig. Figure 17.3 shows some (arbitrary) change in the average price of a product over time.
Since equation (17.2) describes a stochastic process, its solution is a probability density distribution. Equation (17.5) reflects the fact that each price for a product at some moment t has its own probability density p.
The epistemological need for experience to objectify assessments is confirmed by their probabilistic (stochastic) nature. The increase in the number of agreements or facts of assessment makes it possible to consider them as non-deterministic, namely stochastic quantities, independent of each other and the influence of measurement methods on them. Estimates also become stochastic because their calculations are separated from each other and do not correspond with each other. In fact, in a single valuation agreement, the methods of the buyer and the seller or several experts are agreed upon or at least their results are compared. When there is a multiplicity, territorial and temporal separation of transactions, valuation methods are not compared with each other and it becomes possible to interpret valuations as a stochastic process, as a result of which its mathematical expectation is accepted as an objective assessment.
Collection, processing and summary of information are an integral part of the overall information and analytical marketing process. Obtaining information is subordinated to management tasks and aims to provide assessment and analysis of market processes for making the right marketing decisions. The management process is impossible without understanding the retrospective development of the company, assessing its present and forecasting the future. Regulation of some market processes also requires information about this process itself and the factors influencing it. Information is a means of reducing the uncertainty inherent in stochastic market processes. According to the father of cybernetics N. Wiener, managing a company is the process of converting information into actions. Information is a marketing management tool.
Stochastic processes in inventory management systems. It is usually impossible to specify the exact characteristics of demand. The deterministic description is only an approximation. Delays in deliveries, losses during transportation can be described using probabilistic parameters. Delivery time varies due to variability in order fulfillment time and execution of accompanying documentation.
Let us now consider the behavior model of a potential depositor, that is, a depositor who has not yet opened his account at time to. In this model, it is assumed that the account is opened at some random moment time t > 0 under the influence of circumstances, the appearance of which in time is described by the Poisson stochastic process k+(t) with the intensity parameter R.+. Thus, the random number + (0, t) = k+ (t) - k (t0) occurrences over a period of time of circumstances conducive to opening an account by a potential depositor has a Poisson distribution k+(t0,t)e Pn(k (t-tf >)). To simplify the model, it is assumed that a potential investor cannot open and close his account repeatedly over a period of time.
For economic research great value also has an analysis of stochastic processes, incl. "Markov processes".
In the same way, you can recreate an artificial picture of the work of the store itself, where the distribution of customer approach time will interact with the distribution of service time for an individual customer. We again obtain two stochastic processes. Their interaction will produce a “queue” with approximately the same characteristics (for example, average queue length or average waiting time) as a real queue.
Random (stochastic) processes 294
Cities, especially large ones, contain within their administrative-territorial boundaries a complex complex of continuously occurring stochastic processes of interaction between numerous economic entities with each other and with external counterparties.
Rosenblat-Roth M. Entropy of stochastic processes // DAN USSR, 1957.
STOCHASTIC PROCESSES - events, processes, the course of which is significantly influenced by random factors.
Until recently, the issues of determining the norms of sales reserves in physical terms were not given sufficient attention. Issues of rationing reserves were developed only for two types of material resources - cement and coal. In addition, there is currently a Standard Instruction in force, one of the sections of which regulates the issues of determining the norms of working capital advanced to finished product inventories. In the economic literature, only two works are devoted to the rationing of sales inventories -,. The methodological approaches to determining norms and algorithms recommended in them are given in Table. 3.3, from which it is clear that they differ significantly from each other. For example, if in the Instructions the calculation is based on the assumption that the conditions for the formation of a marketable coal reserve are a stochastic process, and probabilistic processing of variations in the values of standard-forming factors is used, then in other works a deterministic approach to calculation is used. Authors also have different views on the structure of the calculated norm itself, i.e. economic content of its components. N. Fasolyak suggests that when calculating the norm, it should be determined through the same components as in the case of industrial reserves, but does not disclose their physical content. Other authors take into account all standard-forming factors together, without dividing them into groups.
STOCHASTIC PROCESS - see Random process
Real book is devoted to the presentation of the fractal market hypothesis as an alternative to the efficient market hypothesis. Fractals, as a consequence of the geometry of the Demiurge, are present everywhere in our world and play a significant role, including in the structure of financial markets, which are locally random, but globally determined, according to the author. The book will discuss methods of fractal analysis of stock, bond and currency markets, methods of distinguishing independent process, a nonlinear stochastic process and a nonlinear deterministic process, and examines the impact of these differences on user investment strategies and modeling capabilities. Such strategies and modeling capabilities are closely related to the asset type and investment horizon of the user.
Figures 2.5 and 2.6 show similar distributions for the yen/dollar exchange rate (1971-1990) and 20-year US Treasury yields (1979-1992), respectively. Fat tails are not just a stock market phenomenon. Other capital markets show similar characteristics. Such fat-tailed distributions are often evidence of a long-term memory system produced by a nonlinear stochastic process.
The most popular explanation for scarcity is that returns are mean reverting. A mean-reverting stochastic process can produce a bounded set, but not an increasing Sharpe ratio. Mean reversion implies a zero-sum game. Exceptionally high earnings in one period are offset by below-average earnings in a later period. The Sharpe ratio would remain constant because profits would also be limited. Thus, the average reversion in earnings is not a completely satisfactory explanation for the limited variability. Regardless, the process that produces the observed volatility term structure is clearly non-Gaussian, nor is it well described by a normal distribution.
Why Stocks and Bonds Are Bounded Sets A possible explanation for boundedness is mean-reverting stochasticity, but it does not explain the faster-growing standard deviation. Limits and rapidly increasing standard deviations are usually caused by deterministic systems with periodic or non-periodic cycles.
IN at the moment We can see evidence that stocks, bonds, and currencies are possible nonlinear stochastic processes in the short term, as evidenced by their frequency distributions and volatility term structures. However, stocks and bonds have signs of long-term determinism. Once again we see local randomness and global determinism.
In this book, we will look at methods for distinguishing between an independent process, a nonlinear stochastic process, and a nonlinear deterministic process, and explore how these differences affect our investment strategies and our modeling abilities. Such strategies and modeling capabilities are closely related to the type of asset and our investment horizon.
The next section explores R/S analysis various types time series, which are often used in modeling financial economics, as well as other types of stochastic processes. Special attention attention will be paid to the possibility of a type II error (classifying a process as having long-term memory, whereas in reality, the process has short-term memory).
They are a family of nonlinear stochastic processes, in
Autoregressive (AR) process. A stationary stochastic process, where the current value of a time series correlates with past values p (p is some integer), is called an AR(p) process. When the current value is related to two previous values, we have an AR(2) process. An AR(1) process has infinite memory.
Suffice it to say, except for the formula for FastK (RAW), all these Stochastic functions, and therefore their derived indicators, do not correspond to George Lane's published definition of the Stochastic Process, representing modifications of the original formula. Be sure to check the lists of these features using TradeStaton's PowerEditor to see what exactly you are using before you make trading decisions based on these indicators.
Stochastics (from the Greek Sto hasis - guess) - the probability of events caused by a random combination of factors. A stochastic (possible, probable) set is formed as a result of the implementation of a stochastic process and is a set possible combinations selected units.
STOCHASTIC PROCESS - a process is called stochastic if it is described by random variables whose values change over time. See Random process for more details.
RANDOM PROCESS, probabilistic process, stochastic process (sto hasti pro ess) - a random function X(t) from the real time parameter teT, the values of which for any t are random variables. The domain of definition C p is either a sequence or a finite or infinite interval , in the first case C p is called a process with discrete time, in the second - a process with continuous time. An example of C p is a flow
- STOCHASTIC PROCESS
same as random... - STOCHASTIC PROCESS
process is the same as a random process... - PROCESS
FORMULARY - see FORMULAR PROCESS... - PROCESS in the Dictionary of Economic Terms:
CRIMINAL - see CRIMINAL PROCEDURE... - PROCESS in the Dictionary of Economic Terms:
TOKYO - see TOKYO PROCESS... - PROCESS in the Dictionary of Economic Terms:
TRANSPORTATION - see TRANSPORTATION PROCESS... - PROCESS in the Dictionary of Economic Terms:
NUREMBERG - see NUREMBERG TRIAL... - PROCESS in the Dictionary of Economic Terms:
LEGISACTIONAL - see LEGISACTIONAL... - PROCESS in the Dictionary of Economic Terms:
CONSTITUTIONAL - see CONSTITUTIONAL PROCESS... - PROCESS in the Dictionary of Economic Terms:
ELECTORAL - see ELECTORAL PROCESS... - PROCESS in the Dictionary of Economic Terms:
LEGISLATIVE - see LEGISLATIVE PROCESS... - PROCESS in the Dictionary of Economic Terms:
CIVIL INTERNATIONAL - see INTERNATIONAL CIVIL PROCEDURE... - PROCESS in the Dictionary of Economic Terms:
BUDGET - see BUDGET PROCESS... - PROCESS in the Dictionary of Economic Terms:
ADMINISTRATIVE - see ADMINISTRATIVE... - STOCHASTIC in the Big Encyclopedic Dictionary:
(from the Greek stochastikos - able to guess) random, ... - PROCESS in the Big Encyclopedic Dictionary:
(from Latin processus - advancement) 1) consistent change of phenomena, states in development of something be. 2) A set of sequential actions to achieve some... - PROCESS in Bolshoi Soviet encyclopedia, TSB:
(from Latin processus - advancement), 1) consistent change of states of development stages. 2) A set of sequential actions to achieve a result (for example, ... - PROCESS
[from Latin processus passage, advancement] 1) sequential change of states, close connection stages of development that naturally follow each other, representing a continuous... - STOCHASTIC in the Encyclopedic Dictionary:
oh, oh mat. Random, occurring with a probability that cannot be predicted. C. process. Stochasticity is a property... - STOCHASTIC
STOCHASTIC PROCESS, the same as a random process... - STOCHASTIC in the Big Russian Encyclopedic Dictionary:
STOCHASTIC (from the Greek stochastikos - able to guess), random, ... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS OF 16", October 25-30, 1880 in St. Petersburg, the first major trial of members of the "Nar. Will". Accusation of preparing assassination attempts on the imp. Alexandra II. ... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS OF 14", 24-28.9.1884 in St. Petersburg over members of the "People's Will". Charge of preparing state coup and assassination attempts on the imp. Alexandra II. ... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS 32", in the Senate in 1863-65, on charges of relations with A.I. Herzen and N.P. Ogarev. Ch. accused N.A. Serno-... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS 193" ("Great Process"), 10/18/1877-1/23/1878 in St. Petersburg, the largest political. process in Russia in the 1870s. over the roar populists - participants in the “walk... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS OF 17", 3/28/4/5/1883 in St. Petersburg over members of the "Nar. Will" (5 members, 2 agents of the Executive Committee) on charges of preparing assassinations... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS OF 50", 21.2-14.3.1877 over members of the group of "Muscovites" (including 14 workers, 16 women). 10 people sentenced to miscellaneous terms of hard labor, ... - PROCESS in the Big Russian Encyclopedic Dictionary:
“PROCESS OF 12”, 11/1-9/1884 in Kyiv over members of “Nar. Volya”. V.S. Pankratov was sentenced to 20 years of hard labor, the rest - to miscellaneous. ... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS 27", in St. Petersburg in 1861-1863 in the case of an illegal publishing house and the 1st Free Printing House in Moscow. P.G. Zaichnevsky, V.D. ... - PROCESS in the Big Russian Encyclopedic Dictionary:
"TRIAL OF THE 21st", 5/5-5/6/1887 in St. Petersburg (G.A. Lopatin and others), on charges of belonging to the "People's Will" and the murder of a gendarme lieutenant colonel. ... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS 28", 25.7-5.8.1879 in Odessa over the roar. populists (D.A. Lizogub, S.F. Chubarov, S.Ya. Wittenberg, etc.). Accusation of belonging to... - PROCESS in the Big Russian Encyclopedic Dictionary:
"PROCESS OF 20", 9-15.2.1882 in St. Petersburg over members of the "People's Will" (11 members, 9 agents of the Executive Committee). Charged with preparing 8 assassination attempts... - PROCESS in the Big Russian Encyclopedic Dictionary:
PROCESS (from Latin processus - advancement), sequential. change of phenomena, states in the development of something. The set is consistent. actions to achieve k.-l. result... - PROCESS in the Popular Explanatory Encyclopedic Dictionary of the Russian Language:
-a, m. 1) The course of development of something. phenomena; successive change of states in the development of smth. Historical process. Irreversible process. The process of education. Process … - STOCHASTIC in the Thesaurus of Russian Business Vocabulary:
- STOCHASTIC in the New Dictionary of Foreign Words:
(gr. stochasis guess) random, or probabilistic, for example, p. process - a process whose nature of change over time can be accurately predicted... - STOCHASTIC in the Dictionary of Foreign Expressions:
[ random, or probabilistic, e.g. p. process - a process whose nature of change over time can be accurately predicted... - STOCHASTIC in the Russian Language Thesaurus:
Syn: probabilistic, random Ant: natural, ... - PROCESS in Abramov's Dictionary of Synonyms:
see action, matter, dispute || lead... - STOCHASTIC in the Russian Synonyms dictionary:
Syn: probabilistic, random Ant: natural, ... - STOCHASTIC in the Complete Spelling Dictionary of the Russian Language.
- STOCHASTIC in the Spelling Dictionary.
- PROCESS in Ozhegov’s Dictionary of the Russian Language:
move, development of some or phenomena, a consistent change of states in the development of something P. growth. Creative p. Production p. process! order of proceedings... - STOCHASTIC
(from the Greek stochastikos - able to guess), random, ... - "PROCESS in Modern explanatory dictionary, TSB:
12", 1-9.11.1884 in Kyiv over the members of " People's Will" Sentence: V.S. Pankratov to 20 years of hard labor, the rest to various... - PROCESS in Ushakov’s Explanatory Dictionary of the Russian Language:
process, m. (Latin processus). 1. Progress, development of something. phenomena; a consistent, natural change of states in the development of something. The process of eliminating feudalism and... - RANDOM PROCESS in the Big Encyclopedic Dictionary:
(probabilistic or stochastic), the process of changing the state or characteristics of some system over time under the influence of various random factors, for which ...
Stochastic processes are divided into stationary and non-stationary processes. A stochastic process is stationary if it is in a certain sense in statistical equilibrium, i.e. its properties with probabilistic point vision does not depend on time. The process is not stationary if these conditions are violated.
Important theoretical value have Gaussian processes. These are processes in which any set of observations has a joint normal distribution. As a rule, the term "time series" itself implies that this series is one-dimensional (scalar).
When analyzing economic time series, a distinction is traditionally made between different types evolution (dynamics). These types of dynamics can, generally speaking, be combined. This sets the decomposition of the time series into components or components, which from an economic point of view carry different meaningful loads. There are two types of components: systematic (this is the result of the influence of constantly acting factors on a time series) and random (this is random noise or error that irregularly affects the series).
Let's list the most important components. The systematic ones include the following:
trend - corresponds to a slow change occurring in a certain direction, which persists over a significant period of time. A trend is also called a trend or long-term movement;
cyclical fluctuations are quasiperiodic dynamics faster than a trend, extending beyond a single period and in which there is an increasing phase and a decreasing phase. The time period between two tops or bottoms is considered the cycle length. Cyclic components are influenced by difficult to identify formal methods factors (change political situation, increase or depletion of resources, etc.). Most often the cycle is associated with fluctuations in economic activity;
seasonal variations- correspond to changes that occur regularly throughout the year, week or day, i.e. within one selected period. They are associated with the seasons and rhythms of human activity;
calendar effects are deviations associated with certain predictable calendar events, such as holidays, number of working days per month, leap year, etc.
Systematic components can all be present simultaneously in a time series.
Random components include the following types:
random fluctuations - random movements relative to high frequency. They are generated by the influence of heterogeneous events on the value being studied (non-systematic or random effect). This component is often called noise (this term comes from technical applications).
outliers are anomalous movements in a time series associated with rarely occurring events that sharply, but only very briefly, deviate the series from common law along which it moves.
structural shifts are anomalous movements in a time series associated with rarely occurring events, which have an abrupt nature and change the trend.
Some economic series can be considered to represent certain types of such movements almost in their pure form. But most has a lot of them complex look. They may exhibit, for example, both a general increasing trend and seasonal changes, which may be superimposed by random fluctuations. It is often useful to analyze individual components in isolation for time series analysis.
In order to be able to decompose specific series on these components, it is necessary to make some assumptions about what properties they should have. It is advisable to first build a formal statistical model that would include these components in some form, then evaluate it, and then, based on the obtained estimates, isolate the components. However, building a formal model is a challenging task. In particular, it is not always clear from the content description how to model certain components. For example, a trend can be deterministic or stochastic. Likewise, seasonal variations can be combined using deterministic variables or using a stochastic process a certain type. The components of a time series can be included in it additively or multiplicatively, or in a mixed form. Moreover, not all time series have sufficient simple structure, so that they can be decomposed into the indicated components. There are two main approaches to decomposing time series into components. The first approach is based on using multiple regressions with factors that are functions of time, the second is based on the use of linear filters.
More articles on economics
Comprehensive economic analysis of the economic activities of the enterprise JSC Russian Railways
Any enterprise is faced with the need to analyze its financial and economic activities. The results of such an analysis allow us to assess the current financial status...
Keynesian and neo-Keynesian concept of economic development
Since the birth of economics as a science, one of the most important discussions has been about the question: “Is there a tendency in the economy to long-term equilibrium with full...
Use of fixed assets at OJSC Guryev Food Processing Plant
The formation of an innovative economy at the present stage of development is becoming a necessary condition for the transition to progressive structural, technological and organizational forms...
As Ross Ashby noted long ago, no system (neither computer nor organism) can produce anything. new, if this system does not contain some source of randomness. In a computer this will be a generator random numbers, thanks to which the “search” of the machine by trial and error ultimately exhausts all the possibilities of the studied area.
In other words, everyone who creates something new, that is, creative systems are, in the language of Chapter 2, divergent; on the contrary, sequences of events that are predictable are, ipso facto*, convergent.
By the way, this does not mean that all divergent systems are stochastic. To do this, the process requires not only access to chance, but also a built-in comparison device, called "natural selection" in evolution, and "preference" or "reinforcement" in thinking.
It is quite possible that from the point of view of eternity, that is, in a cosmic and eternal context, All sequences of events become stochastic. From this point of view, or even from the point of view of a calmly sympathetic Taoist saint, it is perhaps clear that there is no need for any final preference to guide the whole system. But we live in limited area universe, and each of us exists in a limited time. For us, divergence is real and a potential source of disorder or innovation.
Sometimes I even suspect that we, although bound by illusion, do for the Taoist who looks from the outside, this work of choice and preference. (I remember a certain poet who refused military service. He allegedly stated: “I am the civilization that these guys are fighting for.” Maybe he was right in some sense?).
One way or another, apparently, we exist in a limited biosphere, where the main direction is determined by two coupled stochastic processes. Such a system cannot remain unchanged for long. But speed changes are limited by three factors:
A. The Weismann barrier separating somatic from genetic change, discussed in Section 1 of this chapter, ensures that somatic adaptation does not become recklessly irreversible.
b. In each generation, sexual reproduction ensures that the plan new cell, contained in DNA, will not come into sharp conflict with the old plan, that is, with the form of natural selection operating at the level of DNA, no matter what this deviating new plan may mean for the phenotype.
V. Epigenesis acts as a convergent and conserved system; embryonic development, in itself, constitutes a selection context that favors conservatism.
The fact that natural selection there is a conservative process, Alfred Russell Wallace first realized. We have already mentioned earlier, on a different occasion, the relevant quasi-cybernetic model from his letter to Darwin explaining his idea:
“This principle operates exactly like that of the centrifugal governor of a steam engine, which checks and corrects all deviations almost before they become apparent; Likewise, in the animal kingdom, no deviation from equilibrium can ever reach any noticeable magnitude, since it would be felt at the very first step, making existence difficult and subsequent extinction almost inevitable.”
9. comparison and combination of both stochastic systems
In this section I will attempt to clarify the description of both systems, explore the functions of each of them, and finally explore the character of the larger system of general evolution representing the combination of these two subsystems.
Each subsystem has two components (as implied by the word stochastic) (see Dictionary): a random component and the selection process acting on the products of the random component.
In the stochastic system to which Darwinists devoted greatest attention, the random component is genetic change, by mutation or by rearrangement of genes between members of a population. I assume that the mutation does not respond to environmental demands or to internal stresses of the body. But at the same time, I assume that the selection mechanism acting on a randomly changing organism includes both the internal stresses of each creature and, further, the environmental conditions acting on this creature.
The first thing to note is that since embryos are protected by the egg or the mother's body, the external environment does not have a strong selective influence on genetic innovation until epigenesis has passed through a number of stages. In the past, as still today, external natural selection favored changes that protected the embryo and young individual from external dangers. The result was an ever-increasing separation of the two stochastic systems.
An alternative method to ensure the survival of at least some of the offspring is to greatly multiply their number. If in each reproductive cycle an individual produces millions embryos, then the younger generation can endure accidental killing, especially one that leaves only a few individuals out of a million alive. This means a probabilistic attitude towards external reasons death, without any attempt to adapt to their private nature. With this strategy, internal selection is also able to control change unhindered.
Thus, due to the protection of immature descendants, or due to the astronomical multiplication of their number, it turned out that in our time, for many organisms, a new form must first of all submit to the restrictions arising from internal conditions. Will the new form be viable in this environment? Will the developing embryo be able to bear the new form, or will the change entail lethal deviations in the development of the embryo? The answer will depend on the somatic flexibility of the embryo.
Moreover, in sexual reproduction, the combination of chromosomes during fertilization inevitably leads to a process of comparison. Whatever is new in the egg or sperm must meet the old in its partner, and this test favors conformity and immutability. An innovation that is too dramatic will be eliminated as incompatible.
The process of fusion in reproduction is followed by all the complexities of development, and here the combinatorial aspect of embryology, emphasized by the term epigenesis*, requires further conformity testing. As we know, in the status quo ante¦ all compatibility requirements were satisfied to produce a sexually mature phenotype. If this were not so, then the status quo ante would never have existed.
It is very easy to fall into the misconception that the viability of the new means that there was something wrong with the old. This view, to which organisms already suffering from the pathologies of too fast, reckless social change, Certainly, mostly wrong. Always you need to be sure that it's new no worse old We are still not sure that a society with engines internal combustion viable, or that electronic communications such as television are compatible with the aggressive intraspecific competition generated by the Industrial Revolution. All other things being equal (which rarely happens), something old that has been tested to some extent can be considered more viable than something new that has not been tested at all.
Thus, internal selection is the first series of tests of any new genetic component or combination.
In contrast, the second stochastic system has its direct roots in external fitness (i.e., the interaction between phenotype and environment). The random component is delivered here by a system consisting of a phenotype interacting with the environment.
Particular acquired characteristics caused by a reaction to some given environmental change can be predictable. If food delivery is reduced, the body is likely to lose weight, mainly due to the metabolism of its own fats. Exercise and lack of exercise cause changes in the development or underdevelopment of individual organs, and so on. Likewise, individual changes in the environment can often be predicted: climate change towards cooling can be predicted to reduce local biomass, and thereby reduce the supply of food to many species of organisms. But together phenotype and organism produce something unpredictable. Neither the body nor its environment has no information about what the partner will do in the next step. But this subsystem already has a selection component, to the extent that somatic changes caused by habit and environment (including the habit itself) are adaptive. (A broad class of changes induced by environment and experience that are neither adaptive nor pro-survival are known as addiction).
Environment and physiology together offer somatic changes that may or may not be viable, and their viability is determined current state organism, which determines genetics. As I explained in section 4, the limits that somatic change or learning can achieve are ultimately determined by genetics.
As a result, the combination of phenotype and environment constitutes a random component of the stochastic system, which offers change; and the genetic condition has, allowing some changes and prohibiting others. Lamarckians would like somatic changes to control genetics, but the opposite is true. It is genetics that limits somatic changes, making some possible and others impossible.
Moreover, the genome of an individual organism, where the possibilities of change are contained, is what computer engineers would call data bank– it provides a supply of available alternative ways of adaptation. In a given individual, most of these alternatives remain unused and therefore invisible.
Similarly, in another stochastic system the genome populations is now thought to be extremely heterogeneous. All possible genetic combinations, even rare ones, are created by the rearrangement of genes during sexual reproduction. Thus, there is a vast supply of alternative genetic pathways that a natural population can take under selective pressure, as demonstrated by Waddington's studies of genetic assimilation (discussed in Section 3).
If this picture is correct, then both the population and the individual are ready for change. It may be assumed that there is no need to wait for the proper mutations, and this is of some historical interest. As we know, Darwin wavered in his views on Lamarckism, believing that geological time was not sufficient for the process of evolution to operate without Lamarckian heredity. Therefore, in further editions of the Origin of Species, he accepted Lamarck's position. The discovery of Theodosius Dobzhansky that the unit of evolution is the population, and that the population represents a heterogeneous repository of genetic possibilities, greatly reduces the time required by evolutionary theory. The population is able to immediately respond to environmental pressure. The individual organism has the capacity for adaptive somatic change, but it is the population, through the selective elimination of individuals, that makes the change that is transmitted to future generations. The subject of selection becomes opportunity somatic change. Selection carried out by the environment acts on populations.
We now turn to examine individual contributions to general process evolution of each of these two stochastic systems. It is clear that in each case the direction of changes that ultimately enter into the overall picture is determined by the selective component.
The time structure of the two stochastic processes is necessarily different. In a random genetic change, the new state of DNA exists from the moment of fertilization, but may not contribute to external adaptation until much later. In other words, the first test of a genetic change is a test conservatism. Consequently, it is precisely this internal stochastic system that guarantees the formal similarity of internal relations between parts (i.e., homology) that is so noticeable in all cases. In addition, it is possible to predict which of the many types of homology will be most favored by internal selection; answer first of all– cytological: this is the most striking similarity that connects the whole world of cellular organisms. Wherever we look, we find comparable forms and processes in cells. The dance of chromosomes, mitochondria and other organelles of the cytoplasm, the uniform ultramicroscopic structure of flagella wherever they are found, both in plants and animals - all these profound formal similarities are the result of internal selection insisting on conservatism at this elementary level.
The question of future fate changes that survived the first cytological tests. Change affecting earlier stage of the embryo's life, should disrupt a longer and, accordingly, more complex chain further developments. It is difficult or impossible to provide any quantitative estimates of the distribution of homologies in the history of organisms. When it is said that homology is most pronounced at the earliest stages of gamete production, fertilization, and so on, this means some quantitative statement about degrees homology, which gives meaning to characteristics such as chromosome number, mitotic patterns, bilateral symmetry, limbs with five fingers, central nervous system with the spinal cord, and so on. Such estimates are, of course, highly artificial in a world where (as noted in Chapter 2) quantity never determines pattern. But the intuitive feeling still remains. The only ones formal patterns shared by everyone cellular organisms– both plants and animals – are at the cellular level.
An interesting conclusion emerges from this line of thought: After all the controversy and doubt, the recurrence theory deserves support. There is a priori reason to expect that embryos will more closely resemble in their formal patterns the embryonic forms of their ancestors than do adults resemble the forms of their adult ancestors. This is far from what Haeckel and Herbert Spencer dreamed of, who imagined that embryology should follow the path of phylogenesis. Modern formulation more negative: Deviation from the beginning of the path is more difficult (less likely) than deviation from later stages. If we, as evolutionary engineers, were faced with the task of choosing a phylogenetic path from free-swimming, tadpole-like organisms to sessile, worm-like, mud-dwelling organisms Balanoglossus, then we would find that the easiest path of evolution would be to avoid too early or too severe disturbances in the embryonic stage. Maybe we'd even find that evolutionary the process is simplified by subdividing epigenesis by distinguishing the individual stages. We would then arrive at an organism with free-swimming, tadpole-like embryos that at some point metamorphose into worm-like, sessile adults.
The mechanism of variability does not simply resolve, and does not simply create. It has a continuous determinism, where possible changes amount to Class changes suitable for this mechanism. The system of random genetic changes, filtered by the selective process of internal viability, gives phylogeny the character of ubiquitous homology.
If we now consider the second stochastic system, we arrive at a completely different picture. Although no learning or somatic change can directly affect DNA, the obvious fact is that somatic changes (ie the notorious acquired traits) are usually adaptive. In terms of individual survival and/or reproduction and/or simple comfort and stress reduction, adaptation to environmental changes is beneficial. This adjustment occurs at many levels, but at each level there is a real or perceived advantage. It's a good idea to breathe faster when you get to higher altitudes; It's also a good idea to learn to cope without shortness of breath if you have to stay in the mountains for a long time. It is a good idea to have a physiological system that can adapt to physiological stress, although such adaptation leads to acclimation, and acclimation can become addictive.
In other words, somatic adaptation always provides the context for genetic change, but whether such genetic change then occurs is another matter entirely. I will leave this question aside for now and consider the range of genetic changes May be suggested by somatic change. Of course, this spectrum or this set of possibilities sets an outer limit to what a given stochastic component of evolution can achieve.
One common feature somatic variability is immediately obvious: All such changes - quantitative or - as computer engineers would say - analog. In an animal body, the central nervous system and DNA are largely (perhaps completely) discrete, but the rest of the physiology is analog.
Thus, comparing random genetic changes the first stochastic system with the reactive somatic changes of the second, we again encounter the generalization emphasized in Chapter 2: Quantity does not determine the pattern. Genetic changes may be highly abstract, may operate at a distance of many stages from their final phenotypic expression, and, of course, in their final expression may be both quantitative and qualitative. But somatic changes are much more immediate and, I believe, purely quantitative. As far as I know, descriptive sentences that introduce into the description of a species patterns common to other species (i.e., homologies) are never violated by somatic changes that habit and environment can produce.
In other words, the contrast demonstrated by D'Arcy Thompson (see Fig. 9) appears to have its roots in (i.e., follows from) the contrast between the two great stochastic systems.
Finally, I must compare the processes of thought with the double stochastic system of biological evolution. Is such a dual system also inherent in thinking? (If this is not the case, then the entire structure of this book becomes questionable.)
First of all, it is important to note that “Platonism,” as I called it in Chapter 1, is made possible today by arguments that are almost the opposite of those that dualistic theology would favor. The parallelism between biological evolution and mind (mind) is created not by postulating an Engineer or Master hiding in the mechanism of the evolutionary process, but, on the contrary, by postulating the stochasticity of thinking. Darwin's nineteenth-century critics (notably Samuel Butler) wanted to introduce into the biosphere what they called "mind" (i.e., supernatural entelechy). Nowadays I would emphasize that creative thought always contains a random component. The research process is an endless process trial and error mental progress – can achieve new only by entering on randomly emerging paths; some of them, when tested, are somehow selected for something like survival.
If we assume a fundamentally stochastic nature creative thinking, then a positive analogy arises with several aspects of the human mental process. We are looking for a binary division of the thinking process, stochastic in both its halves and such that the random component of one half must be discrete, and the random component of the other half must be analog.
It seems that the simplest way to approach this problem is to consider first the processes of selection that determine and limit its results. Here we encounter two main ways of testing thoughts or ideas.
The first is the test of logical coherence: does the new idea make sense in light of what is already known or what we believe? Although there are many kinds of meaning, and although “logic,” as we have already seen, represents only a poor model of how things are in the world, yet the first requirement of the thinker for the concepts arising in his mind remains something like coherence or coherence - strict or imaginary. On the contrary, the generation of new concepts depends almost entirely (though perhaps not entirely) on the rearrangement and new combination of existing ideas.
Indeed, there is a remarkably close parallel between the stochastic process that occurs inside the brain and another stochastic process - the genesis of random genetic changes, the results of which are worked on by a process of internal selection that ensures some correspondence between old and new. And upon closer examination of this subject, the formal similarity seems to increase.
Discussing the contrast between epigenesis and creative evolution, I pointed out that in epigenesis everything new information must be left aside, and that the process is more like deducing theorems within the framework of some initial tautology. As I have noted in this chapter, the entire process of epigenesis can be regarded as a filter, precisely and unconditionally requiring the growing individual to conform to certain standards.
So, we notice that in the intracranial thinking process there is a similar filter, which, like epigenesis in individual organism, demands obedience and enforces this demand through a process more or less reminiscent of logic (i.e., similar to the construction of a tautology to create theorems). In the process of thinking severity similar internal coherence in evolution.
In summary, the intracranial stochastic system of thinking or learning closely resembles that component of evolution in which random genetic changes are selected by epigenesis. Finally, the cultural historian has at his disposal a world in which formal similarities persist through many generations of cultural history, so that he can look for corresponding patterns there in the same way as a zoologist looks for homologies.
Turning now to another process of learning or creative thinking, involving not only the individual's brain, but also the world around the organism, we find an analogue of this process in evolution, where experience creates that relationship between the organism and the environment, which we call device, imposing changes in habits and soma on the body.
Every action of a living organism involves some degree of trial and error, and for a trial to be new, it must be to some extent random. Even if the new action is only an element of some well-studied class action, yet, since it is new, it must become to some extent a confirmation or exploration of the proposition “it is done like this.”
But in learning, as in somatic change, there are limitations and facilitations that select what can be learned. Some of them are external to the body, others are internal. In the first case, what can be learned at a given moment is limited or facilitated by what has been learned before. In reality, there is also learning how to learn—with a finite limit determined by genetic makeup—that which can be immediately changed in response to environmental demands. And at each step, genetic control is ultimately at work (as noted in the discussion of somatic variation in section 4).
Finally, it is necessary to compare both stochastic processes, which I separated for the purpose of analysis. What formal relationship exists between them?
As I understand it, the crux of the matter is the contrast between discrete and analog, or, in another language, between name and called process.
But naming is itself a process, and a process that occurs not only in our analysis, but also, in a deep and significant way, in the very systems we are trying to analyze. Whatever the coding and mechanical relations between DNA and phenotype, DNA is still in some way an administrative organ, prescribing - and in this sense naming - the relations that should appear in the phenotype.
But if we admit that naming is a phenomenon that occurs in the phenomena we study and organizes them, then we admit ipso facto that we expect to find in this phenomenon a hierarchy of logical types.
Up to this point we can make do with Russell and Principia.¦ But now we are no longer in the Russellian world of abstract logic and mathematics, and cannot accept an empty hierarchy of names or classes. Mathematics is easy to talk about names names names or about classes classes classes. But for the scientist this empty world is not enough.+ We are trying to understand the interweaving or interaction of discrete stages (i.e. names) with analog stages. The naming process itself is called, and this fact forces us to replace alternating simple ladder of logical types offered by Principia.
In other words, to reunite two stochastic systems, into which I divided for the purpose of analysis both evolution and mental process, I'll have to look at both in alternating order. What's in Principia appears as a ladder of steps of one type (names of names of names, and so on), becomes an alternation of steps of two types. To come from name To name name, we have to go through process naming names. There must always be a generation process creating classes before they can be named.
This very broad and complex subject will be covered in Chapter 7.
The word stochastic is used by mathematicians and physicists to describe processes in which there is an element of randomness. It comes directly from Greek word“atoaaiizeoa.” In Aristotle's ethics the word is used in the sense of "the ability to guess." Mathematicians used this word, apparently on the grounds that when it is necessary to guess, an element of chance appears. Webster's New International Dictionary defines stochastic as conjectural. We thus notice that the technical meaning of this word is not in exact accordance with its lexical (dictionary) definition. In the same sense as “stochastic process,” some authors use the expression “random process.” In the future, we will talk about processes and signals that are not purely random, but contain randomness to one degree or another. For this reason we prefer the word "stochastic".
Rice. 3.1-1. Comparison of typical stochastic and predictable signals.
In Fig. 3.1-1 are compared simple shapes fluctuations of stochastic and regular signals. If we repeat the experiment of measuring a stochastic signal, we will obtain oscillations of a new form, different from the previous one, but still showing some similarity in characteristic features. Recording ocean wave vibrations
is another example of a stochastic signal. Why is it necessary to talk about these rather unusual stochastic signals? The answer to this question is based on the fact that the input signals of automation systems are often not completely predictable, like a sine wave or a simple transient. In fact, stochastic signals are encountered more often in studies of automatic systems than predictable signals. However, the fact that predictable signals have been important so far is not a serious omission. Quite often it is possible to arrive at an acceptable technique by selecting signals from the class of predictable signals so as to reflect the characteristic features of the true signal, which is stochastic in nature. An example of this kind is the use of several suitably selected sinusoids to represent stochastic changes in the moments that cause pitching in a ship stability problem. On the other hand, we encounter problems in which it is very difficult to represent a true stochastic signal using a predictable function. As a first example, consider the diagram of an automatic target tracking and fire control system. Here, the radar guidance device does not measure the guidance error precisely, but only approximately. The difference between the true pointing error and what the radar measures is often called radar noise. It is usually very difficult to approximate radar noise with a few sinusoids or other simple functions. Another example is the weaving of textile fibers. During the weaving process, a thread is drawn from randomly tangled bundles of fiber (called yarn). Thread thickness, in a sense, can be considered as an input signal when regulating the weaving process. Deviations in this process occur due to changes in the number and thickness of individual fibers in different interwoven sections of the yarn. Obviously, this type of deviation is stochastic in nature, and it is difficult to approximate it with any regular functions.
The previous discussions show that stochastic signals play a role in the study of control systems important role. So far we have talked about stochastic signals as signals caused by processes containing some element of randomness. To proceed further, we must clarify the concepts of such signals. Modern physics, especially quantum mechanics, teaches that everything physical processes upon detailed study
turn out to be discontinuous and indeterministic. Laws classical mechanics are replaced by statistical laws based on the probability of events. For example, we usually consider the voltage of oscillations occurring on the screen of an oscilloscope vacuum tube as smooth function. However, we know that if we examine these vibrations using a microscope, they will not look so smooth due to the shot noise in the tube that accompanies the excitation of the vibrations. After some thought, it is not difficult to come to the conclusion that all signals in nature are stochastic. Although we first assumed that, compared to a sine wave or unit jump function, a stochastic signal is relatively abstract concept, but in reality the opposite is true: the sinusoid, the unit jump function and regular signals in general represent an abstraction. However, like Euclidean geometry, it is a useful abstraction.
A stochastic signal cannot be represented graphically in a predetermined manner, since it is caused by a process containing an element of randomness. We cannot say what the magnitude of the stochastic signal is at a future time. About a stochastic signal at a future time, we can only say what is the probability that its value falls within a certain interval. We thus see that the concepts of function for a stochastic signal and for a regular signal are completely different. For regular variable size the idea of a function implies a certain dependence of a variable on its argument. With each argument value we associate one or more variable values. In the case of a stochastic function, we cannot uniquely connect the value of a variable with some particular value of the argument. All we can do is associate some probability distributions with the particular values of the argument. In a certain sense, all regular signals are the limiting case of stochastic signals when the probability distributions have high peaks, so that the uncertainty in the position of the variable for the partial value of the argument is zero. At first glance, a stochastic variable may seem so uncertain that its analytical consideration is impossible. However, we will see that analysis of stochastic signals can be done using probability density functions and other statistical characteristics such as averages, root mean squares, and correlation functions. Due to their statistical nature, it is often convenient to consider stochastic signals as elements of many signals, each of which is caused by the same process. This set of signals is called an ensemble. The concept of an ensemble for stochastic signals corresponds to the concept of a population in statistics. Characteristics of a stochastic signal
usually refer to the ensemble, and not to a particular signal of the ensemble. So when we talk about certain properties stochastic signal, we usually assume that the ensemble has these properties. In general, it is impossible to consider that an individual stochastic signal has arbitrary properties(with the possible exclusion of non-essential properties). In the next paragraph we will discuss an important exception to this general rule.
