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Approximation of the marginal distributionsof a semi-Markov process using a finite volume scheme

Published online by Cambridge University Press:  15 October 2004

Christiane Cocozza-Thivent  and
Robert Eymard
Christiane Cocozza-Thivent
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées (UMR 8050 CNRS), Université de Marne la Vallée, Cité Descartes, 5 boulevard Descartes, Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France. cocozza@univ-mlv.fr., eymard@univ-mlv.fr.
Robert Eymard
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées (UMR 8050 CNRS), Université de Marne la Vallée, Cité Descartes, 5 boulevard Descartes, Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France. cocozza@univ-mlv.fr., eymard@univ-mlv.fr.
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Abstract

In the reliability theory, the availability ofa component, characterized by non constant failure and repair rates,is obtained, at a given time, thanks to the computation of the marginal distributions of asemi-Markov process. These measures are shown to satisfy classicaltransport equations, the approximation of which can be donethanks to a finite volume method.Within a uniqueness result for the continuous solution,the convergence of the numerical scheme isthen proven in the weak measure sense,and some numerical applications, which show the efficiency and theaccuracy of the method, are given.

Keywords

Renewal equationsemi-Markov processconvergence of a finite volume scheme.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 5 , September 2004 , pp. 853 - 875
Copyright
© EDP Sciences, SMAI, 2004

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