Stochastic Comparisons between hitting times for Markov Chains and words' occurrences

Emilio De Santis, Fabio Spizzichino

Published 2012-10-03, updated 2014-03-24Version 2

We develop some sufficient conditions for the stochastic ordering between hitting times, in a fixed state, for two Markov chains. In particular, we focus attention on the so called \emph{skip-free} case. In the analysis of such a case, we develop a special type of coupling. We also compare different types of relations between two, non-necessarily skip-free, Markov chains on the same state space. Such relations have a natural role in establishing the usual and the asymptotic stochastic ordering between the probability distributions of hitting times. Finally, we present some discussions and examples related with words' occurrences.