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

Assure Hull Summing 

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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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