First hitting probabilities for semi-Markov chains and estimation |
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Authors: | Stylianos Georgiadis |
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Affiliation: | Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, Denmark |
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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. |
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Keywords: | Absorption probability asymptotic properties first hitting probability non-parametric estimator semi-Markov chains. |
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