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A sequential particle algorithm that keeps the particle system alive

François Le Gland 1 Nadia Oudjane 2, 3 
1 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 : A sequential particle algorithm proposed by Oudjane (2000) is studied here, which uses an adaptive random number of particles at each generation and guarantees that the particle system never dies out. This algorithm is especially useful for approximating a nonlinear (normalized) Feynman-Kac flow, in the special case where the selection functions can take the zero value, e.g. in the simulation of a rare event using an importance splitting approach. Among other results, a central limit theorem is proved by induction, based on the result of Rényi (1957) for sums of a random number of independent random variables. An alternate proof is also given, based on an original central limit theorem for triangular arrays of martingale increments spread across generations with different random sizes.
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François Le Gland, Nadia Oudjane. A sequential particle algorithm that keeps the particle system alive. Blom, Henk A. P. and Lygeros, John. Stochastic hybrid systems: Theory and safety critical applications, 337, Springer, pp.351-389, 2006, Lecture Notes in Control and Information Sciences, ⟨10.1007/11587392_11⟩. ⟨hal-00912079⟩



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