ESTIMATION OF THE STATIONARY DISTRIBUTION OF A SEMI-MARKOV CHAIN

Vlad Stefan  Barbu; Jan  Bulla; Antonello  Maruotti

Vlad Stefan Barbu Université de Rouen, Laboratoire de Mathématiques Raphaël Salem, UMR 6085, Avenue de l' Université, BP.12, F76801 Saint-Étienne-du-Rouvray, France
Jan Bulla Université de Caen, Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139, 14032 Caen Cedex, France
Antonello Maruotti Università di Roma Tre, Dipartimento di Istituzioni Pubbliche, Economia e Società, Rome, Italy

Keywords: semi-Markov chains, stationary distribution, nonparametric estimation, asymptotic properties

Abstract

This article is concerned with the estimation of the stationary distribution of a discretetime semi-Markov process. After briefly presenting the discrete-time semi-Markov setting, we propose an estimator of the associated stationary distribution. The main results concern the asymptotic properties of this estimator, as the sample size becomes large. A numerical example illustrates the asymptotic properties of the estimators.

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