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Discrete-Parameter Controlled Stochastic Processes

  • Iosif Il’ich Gihman
  • Anatoliĭ Vladimirovich Skorohod

Abstract

Let two sets X and U with σ-algebras of measurable subsets \( \mathfrak{A}\;and\;\mathfrak{B} \) respectively, i.e. two measurable spaces \( (X,\mathfrak{A})\;and\;(U,\mathfrak{B}) \) be given. The first space is called the phase space of the basic process and the second the phase space of control. Let N be the set of non-negative integers. In this Chapter all the processes are defined on the set N. To define a controlled process it is necessary to define the probability distribution of a random process with values in X provided a sequence of controls at each instant of time is given and also to define a rule according to which these controls are selected. We shall now describe the components of a controlled process in a more precise manner.

Keywords

Markov Chain Basic Process Control Object Borel Function Lower Semicontinuous Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1979

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

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