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

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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.

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Authors and Affiliations

  1. Université de Technologie de Compiègne, Centre de Recherche de Royallieu, LMAC, BP 20529, 60205, Compiègne cedex, France

    Julien Chiquet & Nikolaos Limnios

  2. Commissariat à l’Énergie Atomique, Centre de Recherche de Saclay, DM2S/SERMA/LCA, 91191, Gif sur Yvette cedex, France

    Julien Chiquet

Authors
  1. Julien Chiquet
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  2. Nikolaos Limnios
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Correspondence to Julien Chiquet.

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Chiquet, J., Limnios, N. Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process. Methodol Comput Appl Probab 8, 431–447 (2006). https://doi.org/10.1007/s11009-006-0423-z

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  • DOI: https://doi.org/10.1007/s11009-006-0423-z

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