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

Julien Chiquet; Nikolaos Limnios

doi:10.1007/s11009-006-0423-z

Methodology and Computing in Applied Probability

December 2006, Volume 8, Issue 4, pp 431–447

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

Authors
Authors and affiliations

Julien ChiquetEmail author
Nikolaos Limnios

Article

First Online:: 01 December 2006

Received:: 25 July 2006
Revised:: 25 July 2006
Accepted:: 04 August 2006

DOI: 10.1007/s11009-006-0423-z

Cite this article as:: Chiquet, J. & Limnios, N. Methodol Comput Appl Probab (2006) 8: 431. doi:10.1007/s11009-006-0423-z

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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.

Keywords

Stochastic dynamical system Markov process Estimation Fatigue crack growth

AMS 2000 Subject Classification

60H10 60K40 62M05

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Authors and Affiliations

Julien Chiquet
- 1
- 2
Email author
Nikolaos Limnios
- 1

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

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

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