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

Christiane Cocozza-Thivent (1) , Robert Eymard (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: finite volume; Renewal equation; semi-Markov process; convergence

Domaines: Physique mathématique [math-ph]

Christiane Cocozza-Thivent, Robert Eymard. Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme. ESAIM: Mathematical Modelling and Numerical Analysis, 2004, 38 (5), pp.853-875. ⟨10.1051/m2an:2004043⟩. ⟨hal-00693113⟩