
Controlled Stochastic Processes PDF
I. I. GihmanThe 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.
control engineers to convert stochastic optimal control into a corresponding deterministic one. One approach to remodel a stochastic process into a deterministic counterpart is using Fokker Planck equation (FPE). FPE is a parabolic PDE that models the time evolution of probability density function (PDF) of a stochastic process. PDF of the
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Stochastic control or stochastic optimal control is a sub field of control theory that deals with the ... The maximization, say of the expected logarithm of net worth at a terminal date T, is subject to stochastic processes on the components of wealth. In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Historically, the ...

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Controlled stochastic process - Encyclopedia of …

Stochastic Processes, Estimation, and Control is divided into three related sections. First, the authors present the concepts of probability theory, random variables, and stochastic processes, which lead to the topics of expectation, conditional expectation, and discrete-time estimation and the Kalman filter. After establishing this foundation STOCHASTIC CONTROL PROBLEMS, VISCOSITY SOLUTIONS, …

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