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ON DISCRETE STOCHASTIC PROCESSES WITH DISJUNCTIVE OUTCOMES

Part of: Control systems Markov processes Discrete mathematics in relation to computer science

Published online by Cambridge University Press:  12 May 2014

KRZYSZTOF LEŚNIAK
KRZYSZTOF LEŚNIAK*
Affiliation:
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland email much@mat.umk.pl
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Abstract

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We introduce a class of discrete-time stochastic processes, called disjunctive processes, which are important for reliable simulations in random iteration algorithms. Their definition requires that all possible patterns of states appear with probability 1. Sufficient conditions for nonhomogeneous chains to be disjunctive are provided. Suitable examples show that strongly mixing Markov chains and pairwise independent sequences, often employed in applications, may not be disjunctive. As a particular step towards a general theory we shall examine the problem arising when disjunctiveness is inherited under passing to a subsequence. An application to the verification problem for switched control systems is also included.

Keywords

disjunctive sequenceBernoulli schemeMarkov chainchain with complete connectionsswitched control systemverification problem

MSC classification

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 68R15: Combinatorics on words 93C30: Systems governed by functional relations other than differential equations (such as hybrid and switching systems)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 1 , August 2014 , pp. 149 - 159
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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