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Article Dans Une Revue Journal of Applied Mathematics and Stochastic Analysis Année : 2006

Characterization of the marginal distributions of Markov processes used in dynamic reliability

Résumé

In dynamic reliability, the evolution of a system is described by a piecewise determinis-tic Markov process (I t ,X t) t≥0 with state-space E × R d , where E is finite. The main result of the present paper is the characterization of the marginal distribution of the Markov process (I t ,X t) t≥0 at time t, as the unique solution of a set of explicit integro-differential equations, which can be seen as a weak form of the Chapman-Kolmogorov equation. Uniqueness is the difficult part of the result.
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Dates et versions

hal-02004712 , version 1 (02-02-2019)

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Christiane Cocozza-Thivent, Robert Eymard, Sophie Mercier, Michel Roussignol. Characterization of the marginal distributions of Markov processes used in dynamic reliability. Journal of Applied Mathematics and Stochastic Analysis, 2006, 2006, pp.1-18. ⟨10.1155/jamsa/2006/92156⟩. ⟨hal-02004712⟩
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