On the Weak Convergence of an Empirical Estimator of the Discrete-Time Semi-Markov Kernel

Stylianos Georgiadis () and Nikolaos Limnios ()
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Stylianos Georgiadis: Université de Technologie de Compiègne Centre de Recherches de Royallieu
Nikolaos Limnios: Université de Technologie de Compiègne Centre de Recherches de Royallieu

Chapter Chapter 14 in Applications of Mathematics and Informatics in Military Science, 2012, pp 221-239 from Springer

Abstract: Abstract In this chapter, we consider the discrete-time semi-Markov processes with finite state space and the empirical estimator of the semi-Markov kernel. The basic definitions concerning the semi-Markov processes are presented. We study the weak convergence of the empirical estimator of the discrete-time semi-Markov kernel. Next, we present the corresponding weak convergence theorem for the empirical estimator of some related measures. The proofs of our results are based on semimartingales.

Keywords: Discrete-time semi-Markov kernel; Empirical estimator; Weak convergence; Invariance principle; Semimartingales (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-4109-0_14

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DOI: 10.1007/978-1-4614-4109-0_14

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