A functional central limit theorem for the empirical estimator of a semi-Markov kernel

Author: Nikolaos Limnios  

Publisher: Taylor & Francis Ltd

ISSN: 1048-5252

Source: Journal of Nonparametric Statistics, Vol.16, Iss.1-2, 2004-02, pp. : 13-18

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Abstract

In this paper we present the invariance principle for the empirical estimator of the semi-Markov kernels and of the conditional transition probabilities for semi-Markov processes with countable state space. The proof is performed through a martingale approach. Finally, an application to alternating renewal process is given.