Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, p. 853-875

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.

DOI : https://doi.org/10.1051/m2an:2004043
Classification:  60K15,  60K20,  65C20,  65M60
Keywords: renewal equation, semi-Markov process, convergence of a finite volume scheme
@article{M2AN_2004__38_5_853_0,
     author = {Cocozza-Thivent, Christiane and Eymard, Robert},
     title = {Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {5},
     year = {2004},
     pages = {853-875},
     doi = {10.1051/m2an:2004043},
     zbl = {1078.60075},
     mrnumber = {2104432},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_5_853_0}
}
Cocozza-Thivent, Christiane; Eymard, Robert. Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 5, pp. 853-875. doi : 10.1051/m2an:2004043. http://www.numdam.org/item/M2AN_2004__38_5_853_0/

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