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

Author

Listed:
  • Christiane Cocozza-Thivent
  • Robert Eymard
  • Sophie Mercier
  • Michel Roussignol

Abstract

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.

Suggested Citation

  • Christiane Cocozza-Thivent & Robert Eymard & Sophie Mercier & Michel Roussignol, 2006. "Characterization of the marginal distributions of Markov processes used in dynamic reliability," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-18, March.
    • Handle: RePEc:hin:jnijsa:092156
    DOI: 10.1155/JAMSA/2006/92156
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    Cited by:

    1. Arismendi, Renny & Barros, Anne & Grall, Antoine, 2021. "Piecewise deterministic Markov process for condition-based maintenance models — Application to critical infrastructures with discrete-state deterioration," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    2. W Lair & S Mercier & M Roussignol & R Ziani, 2011. "Piecewise deterministic Markov processes and maintenance modeling: application to maintenance of a train air-conditioning system," Journal of Risk and Reliability, , vol. 225(2), pages 199-209, June.

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