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2014 A lognormal central limit theorem for particle approximations of normalizing constants
Jean Bérard, Pierre Del Moral, Arnaud Doucet
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Electron. J. Probab. 19: 1-28 (2014). DOI: 10.1214/EJP.v19-3428


Feynman-Kac path integration models arise in a large variety of scientic disciplines including physics, chemistry and signal processing. Their mean eld particle interpretations, termed Diusion or Quantum Monte Carlo methods in physics and Sequential Monte Carlo or Particle Filters in statistics and applied probability, have found numerous applications as they allow to sample approximately from sequences of complex probability distributions and estimate their associated normalizing constants.This article focuses on the lognormal fuctuations of these normalizing constant estimates when both the time horizon n and the number of particles N go to innity in such a way that n/N tends to some number between 0 and 1. To the best of our knowledge, this is the first result of this type for mean field type interacting particle systems. We also discuss special classes of models, including particle absorption models in time-homogeneous environment and hidden Markov models in ergodic random environment, for which more explicit descriptions of the limiting bias and variance can be obtained.


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Jean Bérard. Pierre Del Moral. Arnaud Doucet. "A lognormal central limit theorem for particle approximations of normalizing constants." Electron. J. Probab. 19 1 - 28, 2014.


Accepted: 7 October 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1308.65014
MathSciNet: MR3272327
Digital Object Identifier: 10.1214/EJP.v19-3428

Primary: 65C35
Secondary: 47D08 , 60F05

Keywords: Feynman-Kac formulae


Vol.19 • 2014
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