Electronic Journal of Probability

A lognormal central limit theorem for particle approximations of normalizing constants

Jean Bérard, Pierre Del Moral, and Arnaud Doucet

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 94, 28 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065736

Digital Object Identifier
doi:10.1214/EJP.v19-3428

Mathematical Reviews number (MathSciNet)
MR3272327

Zentralblatt MATH identifier
1308.65014

Subjects
Primary: 65C35: Stochastic particle methods [See also 82C80]
Secondary: 47D08: Schrödinger and Feynman-Kac semigroups 60F05: Central limit and other weak theorems

Keywords
Feynman-Kac formulae

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Bérard, Jean; Del Moral, Pierre; Doucet, Arnaud. A lognormal central limit theorem for particle approximations of normalizing constants. Electron. J. Probab. 19 (2014), paper no. 94, 28 pp. doi:10.1214/EJP.v19-3428. https://projecteuclid.org/euclid.ejp/1465065736


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