AZAÏS, Romain

doi:10.1051/ps/2013054

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AZAÏS, Romain
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]

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ESAIM: Probability and Statistics. 2014, vol. 18, p. 726-749

EDP Sciences

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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.< Réduire

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

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