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

Christiane Cocozza-Thivent, Robert Eymard, Sophie Mercier and Michel Roussignol

International Journal of Stochastic Analysis, 2006, vol. 2006, 1-18


In dynamic reliability, the evolution of a system is described by a piecewise deterministic 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.

Date: 2006
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DOI: 10.1155/JAMSA/2006/92156

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