Christiane Cocozza-Thivent, Robert Eymard, Sophie Mercier, Michel Roussignol, "Characterization of the marginal distributions of Markov processes used in dynamic reliability", International Journal of Stochastic Analysis, vol. 2006, Article ID 092156, 18 pages, 2006. https://doi.org/10.1155/JAMSA/2006/92156
Characterization of the marginal distributions of Markov processes used in dynamic reliability
In dynamic reliability, the evolution of a system is described by a piecewise deterministic Markov process with state-space , where is finite. The main result of the present paper is the characterization of the marginal distribution of the Markov process at time , 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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