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

2012/10/03 by Emilio De Santis, De Santis, Emilio, Fabio Spizzichino +1
Mathematics · #60E15 #60J10 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E15 #msc:60J10

paper · pdf · doi:10.48550/arxiv.1210.1116

20 pages

arxiv created 2014/03/24 · arxiv updated 2014/03/25

Abstract

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 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.

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