A Central Limit Theorem for Fleming-Viot Particle Systems with Hard Killing

Bernard Delyon 1 Frédéric Cérou 2, 1 Arnaud Guyader 3 Mathias Rousset 1, 4
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
4 ASPI - Applications of interacting particle systems to statistics
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : Fleming-Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this context, each particle evolves independently according to the law of the underlying Markov process until its killing, and then branches instantaneously on another randomly chosen particle. While the consistency of this algorithm in the large population limit has been recently studied in several articles, our purpose here is to prove Central Limit Theorems under very general assumptions. For this, we only suppose that the particle system does not explode in finite time, and that the jump and killing times have atomless distributions. In particular, this includes the case of elliptic diffusions with hard killing.
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https://hal.archives-ouvertes.fr/hal-01614094
Contributor : Marie-Annick Guillemer <>
Submitted on : Tuesday, October 10, 2017 - 2:42:55 PM
Last modification on : Tuesday, October 15, 2019 - 4:19:58 PM

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  • HAL Id : hal-01614094, version 1
  • ARXIV : 1709.06771

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Bernard Delyon, Frédéric Cérou, Arnaud Guyader, Mathias Rousset. A Central Limit Theorem for Fleming-Viot Particle Systems with Hard Killing. 2017. ⟨hal-01614094⟩

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