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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