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| HAL: hal-00260732, version 1 |
| DOI: 10.1016/j.spl.2007.12.016 |
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| Statistics and Probability Letters (2007) in press |
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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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Julien Chiquet 1, 2Nikolaos Limnios 1 |
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| (2007-12-28) |
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| 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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| 1: | Laboratoire de Mathématiques Appliquées de Compiègne - EA2222 (LMAC) |
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Université de Technologie de Compiègne |
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| 2: | Laboratoire Statistique et génomes (SG) |
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CNRS : UMR8071 – Institut national de la recherche agronomique (INRA) – Université d'Evry-Val d'Essonne |
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| Subject | : | Mathematics/Probability Mathematics/Dynamical Systems |
| hal-00260732, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00260732 | |
| oai:hal.archives-ouvertes.fr:hal-00260732 | |
| From: Julien Chiquet | |
| Submitted on: Wednesday, 5 March 2008 08:38:28 | |
| Updated on: Wednesday, 5 March 2008 08:38:28 | |
