First hitting probabilities for semi markov chains and estimation

Stylianos Georgiadis

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Abstract

We first consider a stochastic system described by an absorbing semi-Markov chain 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 semi-Markov chain. In the latter case, a nonparametric 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.
Original languageEnglish
JournalCommunications in Statistics: Theory and Methods
Volume46
Issue number5
Pages (from-to)2435-2446
Number of pages23
ISSN0361-0926
DOIs
Publication statusPublished - 2017

Keywords

  • Semi-Markov chains
  • Absorption probability
  • First hitting probability
  • Nonparametric estimator
  • Asymptotic properties

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