First hitting probabilities for semi-Markov chains and estimation

Stylianos Georgiadis

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 5, 2435-2446

Abstract: We first consider a stochastic system described by an absorbing semi-Markov chain (SMC) with finite state space, and we introduce the absorption probability to a class of recurrent states. Afterwards, we study the first hitting probability to a subset of states for an irreducible SMC. In the latter case, a non-parametric estimator for the first hitting probability is proposed and the asymptotic properties of strong consistency and asymptotic normality are proven. Finally, a numerical application on a five-state system is presented to illustrate the performance of this estimator.

Date: 2017
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DOI: 10.1080/03610926.2015.1045080

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