2 edition of **Theory of random functions and its application to control problems** found in the catalog.

Theory of random functions and its application to control problems

V. S. Pugachev

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- 0 Currently reading

Published
**1965**
by Pergamon Press; [U.S.A. ed. distributed by] Addison-Wesley Pub. Co., Reading, Mass. in Oxford, New York
.

Written in English

- Stochastic processes.,
- Control theory.

**Edition Notes**

Statement | [by] V.S. Pugachev. Rev. translation by O.M. Blunn. Translation edited by N.L. Johnson. |

Series | Pergamon Press International series of monographs on automation and automatic control,, v. 5, Pergamon Press international series of monographs on automation and automatic control ;, v. 5., Adiwes international series in mathematics. |

Classifications | |
---|---|

LC Classifications | QA402.3 .P813 1965 |

The Physical Object | |

Pagination | xvii, 833 p. |

Number of Pages | 833 |

ID Numbers | |

Open Library | OL5889571M |

LC Control Number | 63023205 |

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In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random ically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly . Onwards from the mid-twentieth century, the stochastic filtering problem has caught the attention of thousands of mathematicians, engineers, statisticians, and computer scientists. Its applications span the whole spectrum of human endeavour, including satellite tracking, credit risk estimation, human genome analysis, and speech recognition.

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Theory of Random Functions and Its Application to Control Problems presents insights into a branch of probability theory, the theory of random functions, which studies and takes into account the effects of random factors on the functioning of control systems.

The book does not require a high level of competency in the use of mathematical Cited by: Description. Theory of Random Functions and Its Application to Control Problems presents insights into a branch of probability theory, the theory of random functions, which studies and takes into account the effects of random factors on the functioning of control systems.

The book does not require a high level Book Edition: 1. "This book is the first monograph that is completely devoted to the theory of products of random variables (PRV).

It gives the most comprehensive review of the recent results in this area and could be used as a handbook in PRVthe subject index covers the content of the book Cited by: Get this from a library. Theory of random functions and its application to control problems.

[V S Pugachev]. Products of Random Variables: Applications to Problems of Physics and to Arithmetical Functions - CRC Press Book Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory.

V. Pugachev, The theory of random functions and its application to automatic control (GITTL, ). [2] V. Solodovnikov, Introduction to the statistical dynamics of automatic control systems (GITTL, ).Author: G.

Simkin. From an applications viewpoint, the main reason to study the subject of this book is to help deal with the complexity of describing random, time-varying functions. A random variable can be interpreted as the result of a single mea- surement.

The distribution of a single random variable is fairly simple to describe. The theory of random processes is an extremely vast branch of math-ematics which cannot be covered even in ten one-year topics courses with minimal intersection of contents.

Therefore, the intent of this book is to get the reader acquainted only with some parts of the theory. The choice. it is possible to consider random polytopes that appear as convex hulls of any (xed or random) number of points in the Euclidean space.

Example (Random sets related to deterministic and random functions). Let f: Rd 7. R be a deterministic function, and let ˘ be a random variable. If f is continuous, then X= fx: f(x) = ˘gis a random Size: KB. Additional Physical Format: Online version: Pugachev, V.S.

(Vladimir Semenovich). Theory of random functions and its application to control problems. For problems in which uncertainty has been modelled using probability theory in the past, discussions on what approach is right, frequently conclude that both should complement each other.

In the present text, we consider such synergy of fuzzy sets, probability and possibility distributions provided by the concept of a by: 2. viii PREFACE this site, and we invite our readers to submit their contributions. FEATURES Level of rigor and emphasis: Probability is a wonderfully intuitive and applicable ﬁeld of mathematics.

We have tried not to spoil its beauty by presenting too much formal by: Continuous-time random walk 12 Other lattices 14 Other walks 16 Generator 17 Filtrations and strong Markov property 19 A word about constants 21 2 Local Central Limit Theorem 24 Introduction 24 Characteristic Functions and LCLT 27 Characteristic functions of random variables in Rd The goals of this book are to develop an appreciation for the richness and is necessary to avoid problems with a particular R function; these problems are discussed in detail on the website for the text under R Issues.

This fact accounts for the basic engineering Time Series Analysis and Its Applications. book is eminently suitable as a textbook on statistics and probability for engineering students. Areas of practical knowledge based on the fundamentals of probability and statistics are developed using a logical and understandable approach which appeals to the reader’s experience and previous knowledge rather than to rigorous mathematicalFile Size: 2MB.

In experimental work e.g. in physics one often encounters problems where a standard statistical probability density function is applicable. It is often of great help to be able Random. ﬁltering”, and its signiﬁcance is demonstrated on examples. An introduction to stochastic control theory is oﬀered in section 9; we present the principle of Dynamic Programming that characterizes the value function of this problem, and derive from it the associated Hamilton-Jacobi-Bellman equation.

The notion of weakFile Size: KB. In the next sections we will review concepts from Number Theory, the branch of mathematics that deals with integer numbers and their properties. We will be covering the following topics: 1 Divisibility and Modular Arithmetic (applications to hashing functions/tables and simple cryptographic cyphers).Section File Size: KB.

Probability Distributions of Discrete Random Variables. A typical example for a discrete random variable \(D\) is the result of a dice roll: in terms of a random experiment this is nothing but randomly selecting a sample of size \(1\) from a set of numbers which are mutually exclusive outcomes.

Here, the sample space is \(\{1,2,3,4,5,6\}\) and we can think of many different. Optimal Control Theory Version By Lawrence C. Evans Department of Mathematics THE BASIC PROBLEM. Our aim is to ﬁnd a control The next example is from Chapter 2 of the book Caste and Ecology in Social Insects, by G.

Oster and E. Wilson [O-W]. We attempt to model how socialFile Size: KB. Probability theory - Probability theory - Applications of conditional probability: An application of the law of total probability to a problem originally posed by Christiaan Huygens is to find the probability of “gambler’s ruin.” Suppose two players, often called Peter and Paul, initially have x and m − x dollars, respectively.

A ball, which is red with probability p and black with.And welcome to a rather unusual book. Approximation theory is an established ﬁeld, and my aim is to teach you some of its most important ideas and results, centered on classical topics re-lated to polynomials and rational functions.

The style of this book, however, is quite diﬀerent from what you will ﬁnd elsewhere. Everything is illustrated.The course itself consists of two parts: 1) measure theory and integration, and 2) Hilbert space theory, especially the spectral theorem and its applications.

In Chapter II I do the basics of Hilbert space theory, i.e. what I can do without measure theory or the Lebesgue integral. The hero here (and perhapsFile Size: 1MB.