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Methodology and Computing in Applied Probability

, Volume 8, Issue 4, pp 431–447 | Cite as

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

  • Julien ChiquetEmail author
  • Nikolaos Limnios
Article
First Online:

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.

Keywords

Stochastic dynamical system Markov process Estimation Fatigue crack growth 

AMS 2000 Subject Classification

60H10 60K40 62M05 
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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Université de Technologie de Compiègne, Centre de Recherche de Royallieu, LMACCompiègne cedexFrance
  2. 2.Commissariat à l’Énergie Atomique, Centre de Recherche de Saclay, DM2S/SERMA/LCAGif sur Yvette cedexFrance

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