inria-00550716, version 1
Sampling per Mode for Rare Event Simulation in Switching Diffusions
Jaroslav Krystul
a, 1François Le Gland
b, 2Pascal Lezaud
c, 3
N° RR-7499 (2010)
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.
- a – University of Twente
- b – INRIA
- c – DGAC
- 1: Department of Applied Mathematics [Twente]
- University of Twente
- 2: ASPI (INRIA - IRISA)
- CNRS : UMR6074 – INRIA – Université de Rennes 1
- 3: DTI Recherche & Développement (DTI R&D)
- Direction des services de la navigation aérienne – Direction générale de l'Aviation civile
- Domain : Mathematics/Probability
- Keywords : Rare event simulation – Switching diffusion – Multilevel splitting – Stratification – Central limit theorem (CLT)
- Internal note : RR-7499
- inria-00550716, version 1
- http://hal.inria.fr/inria-00550716
- oai:hal.inria.fr:inria-00550716
- From: Francois Le Gland
- Submitted on: Wednesday, 29 December 2010 17:50:01
- Updated on: Thursday, 6 January 2011 12:08:40






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