ON DISCRETE STOCHASTIC PROCESSES WITH DISJUNCTIVE OUTCOMES

Abstract

AbstractWe 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.