Geodesic
Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 5, pp. 853-875

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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 : 10.1051/m2an:2004043
Classification : 60K15, 60K20, 65C20, 65M60
Keywords: renewal equation, semi-Markov process, convergence of a finite volume scheme 
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     title = {Approximation of the marginal distributions of a {semi-Markov} process using a finite volume scheme},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {853--875},
     publisher = {EDP-Sciences},
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     zbl = {1078.60075},
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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 , Tome 38 (2004) no. 5, pp. 853-875. doi: 10.1051/m2an:2004043

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