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Controlled Stochastic Processes

  • Iosif Il’ich Gihman
  • Anatoliĭ Vladimirovich Skorohod

Table of contents

  1. Front Matter
    Pages i-vii
  2. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorohod
    Pages 1-78
  3. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorohod
    Pages 79-115
  4. Iosif Il’ich Gihman, Anatoliĭ Vladimirovich Skorohod
    Pages 116-226
  5. Back Matter
    Pages 227-237

About this book

Introduction

The theory of controlled processes is one of the most recent mathematical theories to show very important applications in modern engineering, parti­ cularly for constructing automatic control systems, as well as for problems of economic control. However, actual systems subject to control do not admit a strictly deterministic analysis in view of random factors of various kinds which influence their behavior. Such factors include, for example, random noise occurring in the electrical system, variations in the supply and demand of commodities, fluctuations in the labor force in economics, and random failures of components on an automated line. The theory of con­ trolled processes takes the random nature of the behavior of a system into account. In such cases it is natural, when choosing a control strategy, to proceed from the average expected result, taking note of all the possible variants of the behavior of a controlled system. An extensive literature is devoted to various economic and engineering systems of control (some of these works are listed in the Bibliography). is no text which adequately covers the general However, as of now there mathematical theory of controlled processes. The authors ofthis monograph have attempted to fill this gap. In this volume the general theory of discrete-parameter (time) controlled processes (Chapter 1) and those with continuous-time (Chapter 2), as well as the theory of controlled stochastic differential equations (Chapter 3), are presented.

Keywords

Kontrolle (Math.) Markov chain Markov process Stochastic processes Stochastischer Prozess diffusion process stochastic process

Authors and affiliations

  • Iosif Il’ich Gihman
    • 1
  • Anatoliĭ Vladimirovich Skorohod
    • 2
  1. 1.Institute of Applied Mathematics and MechanicsAcademy of Sciences of the Ukranian SSRDonetskUSSR
  2. 2.Institute of MathematicsAcademy of Sciences of the Ukranian SSRKievUSSR

Bibliographic information

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