On the optimal importance process for piecewise deterministic Markov process
ESAIM: Probability and Statistics, Tome 23 (2019), pp. 893-921

In order to assess the reliability of a complex industrial system by simulation, and in reasonable time, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems which are modeled by piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space. This reference measure makes it possible to identify the admissible importance processes. Then we derive the characteristics of an optimal importance process, and present a convenient and explicit way to build an importance process based on theses characteristics. A simulation study compares our importance sampling method to the crude Monte-Carlo method on a three-component systems. The variance reduction obtained in the simulation study is quite spectacular.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2019015
Classification : 60K10, 90B25, 62N05
Keywords: Monte-Carlo acceleration, importance sampling, hybrid dynamic system, piecewise deterministic Markovian process, cross-entropy, reliability

Chraibi, H. 1 ; Dutfoy, A. 1 ; Galtier, T. 1 ; Garnier, J. 1

1 
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     author = {Chraibi, H. and Dutfoy, A. and Galtier, T. and Garnier, J.},
     title = {On the optimal importance process for piecewise deterministic {Markov} process},
     journal = {ESAIM: Probability and Statistics},
     pages = {893--921},
     year = {2019},
     publisher = {EDP Sciences},
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     url = {https://www.numdam.org/articles/10.1051/ps/2019015/}
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Chraibi, H.; Dutfoy, A.; Galtier, T.; Garnier, J. On the optimal importance process for piecewise deterministic Markov process. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 893-921. doi: 10.1051/ps/2019015

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