A method to compute the transition function of a piecewise deterministic Markov process with application to reliability

Julien Chiquet; Nikolaos Limnios

doi:10.1016/j.spl.2007.12.016

A method to compute the transition function of a piecewise deterministic Markov process with application to reliability

Julien Chiquet
, Nikolaos Limnios

LMAC – Laboratoire de Mathématiques Appliquées de Compiègne

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We study the time evolution of an increasing stochastic process governed by a first-order stochastic differential system. This defines a particular piecewise deterministic Markov process (PDMP). We consider a Markov renewal process (MRP) associated to the PDMP and its Markov renewal equation (MRE) which is solved in order to obtain a closed-form solution of the transition function of the PDMP. It is then applied in the framework of survival analysis to evaluate the reliability function of a given system. We give a numerical illustration and we compare this analytical solution with the Monte Carlo estimator.

langue originale	Anglais
Pages (de - à)	1397-1403
Nombre de pages	7
journal	Statistics and Probability Letters
Volume	78
Numéro de publication	12
Les DOIs	https://doi.org/10.1016/j.spl.2007.12.016
état	Publié - 1 sept. 2008
Modification externe	Oui

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10.1016/j.spl.2007.12.016

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abstract = "We study the time evolution of an increasing stochastic process governed by a first-order stochastic differential system. This defines a particular piecewise deterministic Markov process (PDMP). We consider a Markov renewal process (MRP) associated to the PDMP and its Markov renewal equation (MRE) which is solved in order to obtain a closed-form solution of the transition function of the PDMP. It is then applied in the framework of survival analysis to evaluate the reliability function of a given system. We give a numerical illustration and we compare this analytical solution with the Monte Carlo estimator.",

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AB - We study the time evolution of an increasing stochastic process governed by a first-order stochastic differential system. This defines a particular piecewise deterministic Markov process (PDMP). We consider a Markov renewal process (MRP) associated to the PDMP and its Markov renewal equation (MRE) which is solved in order to obtain a closed-form solution of the transition function of the PDMP. It is then applied in the framework of survival analysis to evaluate the reliability function of a given system. We give a numerical illustration and we compare this analytical solution with the Monte Carlo estimator.

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A method to compute the transition function of a piecewise deterministic Markov process with application to reliability

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