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

Emilio De Santis; Fabio Spizzichino

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arXiv · 1210.1116

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

Emilio De Santis·Fabio Spizzichino

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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 \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.

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BibTeX RIS

Emilio De Santis, Fabio Spizzichino. 2014-03-24. Stochastic Comparisons between hitting times for Markov Chains and words' occurrences. https://arxiv.org/abs/1210.1116

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