A recursive nonparametric estimator for the transition kernel of a piecewise-deterministic Markov process

Romain Azaïs 1, 2
1 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary piecewise-deterministic Markov process, from only one observation of the path within a long time. In this framework, we do not observe a Markov chain with transition kernel of interest. Fortunately, one may write the transition density of interest as the ratio of the invariant distributions of two embedded chains of the process. Our method consists in estimating these invariant measures. We state a result of consistency under some general assumptions about the main features of the process. A simulation study illustrates the well asymptotic behavior of our estimator.
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Article dans une revue
ESAIM: Probability and Statistics, EDP Sciences, 2014, 18, pp.726-749. 〈10.1051/ps/2013054〉
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https://hal.archives-ouvertes.fr/hal-00759065
Contributeur : Romain Azaïs <>
Soumis le : jeudi 29 novembre 2012 - 23:07:17
Dernière modification le : jeudi 11 janvier 2018 - 06:22:11

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Romain Azaïs. A recursive nonparametric estimator for the transition kernel of a piecewise-deterministic Markov process. ESAIM: Probability and Statistics, EDP Sciences, 2014, 18, pp.726-749. 〈10.1051/ps/2013054〉. 〈hal-00759065〉

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