Sampling per mode for rare event simulation in switching diffusions

Abstract : A straightforward application of an interacting particle system to estimate a rare event for switching diffusions fails to produce reasonable estimates within a reasonable amount of simulation time. To overcome this, a conditional "sampling per mode" algorithm has been proposed by Krystul in [10]; instead of starting the algorithm with particles randomly distributed, we draw in each mode, a fixed number 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 as well as a central limit theorem for the estimate.
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Jaroslav Krystul, François Le Gland, Pascal Lezaud. Sampling per mode for rare event simulation in switching diffusions. Stochastic Processes and their Applications, Elsevier, 2012, 122 (7), pp.2639-2667. ⟨10.1016/j.spa.2012.04.011⟩. ⟨hal-00968683⟩

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