Sampling per mode for rare event simulation in switching diffusions

Jaroslav Krystul 1 François Le Gland 2, * Pascal Lezaud 3
* Corresponding author
2 ASPI - Applications of interacting particle systems to statistics
UR1 - Université de Rennes 1, Inria Rennes – Bretagne Atlantique , CNRS - Centre National de la Recherche Scientifique : UMR6074
Abstract : An interacting particle system (IPS) approach is virtually applicable to estimate rare event for switching diffusions, since these processes own the strong Markov property. Nevertheless, in practice the straightforward application of this approach to switching diffusions fails to produce reasonable estimates within a reasonable amount of simulation time. This happens because each resampling step tends to sample more "heavy" particles from modes with higher probabilities, thus "light" particles in the modes with small probability tend to be discarded. To avoid this, a conditional "sampling per mode" algorithm has been proposed by Krystul (2006): instead of starting the algorithm with particles randomly distributed, we draw in each mode a fixed number of particles and at each resampling step, the same number of particles is sampled for each visited mode. In this paper, we establish a law of large numbers theorem as well as a central limit theorem (CLT) for the estimate of the rare event probability.
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[Research Report] RR-7499, INRIA. 2010, pp.19
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Jaroslav Krystul, François Le Gland, Pascal Lezaud. Sampling per mode for rare event simulation in switching diffusions. [Research Report] RR-7499, INRIA. 2010, pp.19. 〈inria-00550716〉

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