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A finite-volume scheme for dynamic reliability models

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

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