| Issue |
ESAIM: PS
Volume 23, 2019
|
|
|---|---|---|
| Page(s) | 893 - 921 | |
| DOI | https://doi.org/10.1051/ps/2019015 | |
| Published online | 24 December 2019 | |
On the optimal importance process for piecewise deterministic Markov process
1
PERICLES Department, EDF lab saclay,
7 Bd Gaspard Monge,
91120
Palaiseau, France.
2
LPSM (Laboratoire de probabilités, statistique et modélisation), Université Paris Diderot,
75205
Paris Cedex 13, France.
3
CMAP (Centre de mathématiques appliquées), École polytechnique,
91128
Palaiseau Cedex, France.
* Corresponding author: tgaltier@gmail.com
Received:
13
June
2018
Accepted:
3
July
2019
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.
Mathematics Subject Classification: 60K10 / 90B25 / 62N05
Key words: Monte-Carlo acceleration / importance sampling / hybrid dynamic system / piecewise deterministic Markovian process / cross-entropy / reliability
© The authors. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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