On discrete stochastic processes with disjunctive outcomes

Authors

  • K. Lesniak Nicolaus Copernicus University

Keywords:

disjunctive sequence, Bernoulli scheme, Markov chain, chain with complete connections, switched control system, verification problem

Abstract

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 toward general theory we look at the problem when disjunctiveness is inherited under passing to a subsequence. An application to the verification problem for switched control systems is also included. DOI: 10.1017/S0004972714000124

Published

2014-06-03

Issue

Vol. 90 No. 1 (2014)

Section

Articles
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