Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process
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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.
KeywordsStochastic dynamical system Markov process Estimation Fatigue crack growth
AMS 2000 Subject Classification60H10 60K40 62M05
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- J. Chiquet, N. Limnios, and M. Eid, “Modeling and estimating the reliability of stochastic dynamical systems with markovian switching.” In ESREL 2006 - Safety and Reliability for managing Risks, 2006.Google Scholar
- R. Dautray (ed.), Méthodes probabilistes pour les équations de la physique, Synthèse. Eyrolles: Paris, France, 1989.Google Scholar
- M. H. A. Davis, Markov Models and Optimization, Monographs On statistics and Applied Probability 49, Chapman & Hall, UK, 1993.Google Scholar
- W. Härdle, Applied Nonparametric Regression, Econometric Society Monographs, Cambridge University Press, Cambridge, UK, 1990.Google Scholar
- V. S. Korolyuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific: Singapore, 2005.Google Scholar
- H. Tanaka, “Importance sampling simulation for a stochastic fatigue crack growth model,” In R. E. Melchers and M. G. Stewart (eds.), Proceeding of ICASP8 vol. 2, pp. 907–914, 1999.Google Scholar