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Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process

Author

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  • Julien Chiquet

    (Université de Technologie de Compiègne, Centre de Recherche de Royallieu, LMAC
    Commissariat à l’Énergie Atomique, Centre de Recherche de Saclay, DM2S/SERMA/LCA)

  • Nikolaos Limnios

    (Université de Technologie de Compiègne, Centre de Recherche de Royallieu, LMAC)

Abstract

We discuss the use of a continuous-time jump Markov process as the driving process in stochastic differential systems. Results are given on the estimation of the infinitesimal generator of the jump Markov process, when considering sample paths on random time intervals. These results are then applied within the framework of stochastic dynamical systems modeling and estimation. Numerical examples are given to illustrate both consistency and asymptotic normality of the estimator of the infinitesimal generator of the driving process. We apply these results to fatigue crack growth modeling as an example of a complex dynamical system, with applications to reliability analysis.

Suggested Citation

  • Julien Chiquet & Nikolaos Limnios, 2006. "Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 431-447, December.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:4:d:10.1007_s11009-006-0423-z
    DOI: 10.1007/s11009-006-0423-z
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    Cited by:

    1. Chiquet, Julien & Limnios, Nikolaos, 2008. "A method to compute the transition function of a piecewise deterministic Markov process with application to reliability," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1397-1403, September.
    2. Chiquet, Julien & Eid, Mohamed & Limnios, Nikolaos, 2008. "Modelling and estimating the reliability of stochastic dynamical systems with Markovian switching," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1801-1808.
    3. Guglielmo D’Amico & Philippe Regnault, 2018. "Dynamic Measurement of Poverty: Modeling and Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 305-340, November.
    4. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.

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