Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme
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. firstname.lastname@example.org., email@example.com.
Revised: 20 August 2004
In the reliability theory, the availability of a component, characterized by non constant failure and repair rates, is obtained, at a given time, thanks to the computation of the marginal distributions of a semi-Markov process. These measures are shown to satisfy classical transport equations, the approximation of which can be done thanks to a finite volume method. Within a uniqueness result for the continuous solution, the convergence of the numerical scheme is then proven in the weak measure sense, and some numerical applications, which show the efficiency and the accuracy of the method, are given.
Mathematics Subject Classification: 60K15 / 60K20 / 65C20 / 65M60
Key words: Renewal equation / semi-Markov process / convergence of a finite volume scheme.
© EDP Sciences, SMAI, 2004