Discrete-Parameter Controlled Stochastic Processes

Iosif Il’ich Gihman and Anatoliĭ Vladimirovich Skorohod
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Iosif Il’ich Gihman: Academy of Sciences of the Ukranian SSR, Institute of Applied Mathematics and Mechanics
Anatoliĭ Vladimirovich Skorohod: Academy of Sciences of the Ukranian SSR, Institute of Mathematics

Chapter 1 in Controlled Stochastic Processes, 1979, pp 1-78 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1979
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DOI: 10.1007/978-1-4612-6202-2_1

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