BRANDEJSKY, Adrien; DE SAPORTA, Benoîte; DUFOUR, François

doi:10.1239/aap/1331216650

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BRANDEJSKY, Adrien
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]

DE SAPORTA, Benoîte
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Groupe de Recherche en Economie Théorique et Appliquée [GREThA]

DUFOUR, François
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]

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Article de revue

Ce document a été publié dans

Advances in Applied Probability. 2012, vol. 44, n° 1, p. pp196-225

Applied Probability Trust

Résumé en anglais

We present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP). Our approach is based on the quantization of an underlying discrete-time Markov chain related to the PDMP. The approximation we propose is easily computable and is even flexible with respect to the exit time we consider. We prove the convergence of the algorithm and obtain bounds for the rate of convergence in the case of the moments. An academic example and a model from the reliability field illustrate the paper.< Réduire