A finite-volume scheme for dynamic reliability models

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

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

In a model arising in the dynamic reliability study of a system, the probability of the state of the system is completely described by the Chapman-Kolmogorov equations, which are scalar linear hyperbolic partial differential equations coupled by their right-hand side, the solution of which are probability measures. We propose in this paper a finite-volume scheme to approximate these measures. We show, thanks to the proof of the tightness of the approximate solution, that the conservation of the probability mass leads to a compactness property. The convergence of the scheme is then obtained in the space of continuous functions with respect to the time variable, valued in the set of probability measures on R-d. We finally show on a numerical example the accuracy and efficiency of the approximation method.

Mots clés: finite-volume method; Markov processes; dynamic reliability; weak convergence

Domaines: Physique mathématique [math-ph]

Christiane Cocozza-Thivent, Robert Eymard, Sophie Mercier. A finite-volume scheme for dynamic reliability models. IMA Journal of Numerical Analysis, 2005, 26 (3), pp.446-471. ⟨10.1093/imanum/drl001⟩. ⟨hal-00693102⟩