The Annals of Applied Probability

A Berry–Esseen theorem for Feynman–Kac and interacting particle models

Pierre Del Moral and Samy Tindel

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Abstract

In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman–Kac particle approximation models. We design an original approach based on new Berry–Esseen type estimates for abstract martingale sequences combined with original exponential concentration estimates of interacting processes. These results extend the corresponding statements in the classical theory and apply to a class of branching and genealogical path-particle models arising in nonlinear filtering literature as well as in statistical physics and biology.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 1B (2005), 941-962.

Dates
First available in Project Euclid: 1 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1107271673

Digital Object Identifier
doi:10.1214/105051604000000792

Mathematical Reviews number (MathSciNet)
MR2114995

Zentralblatt MATH identifier
1084.82007

Subjects
Primary: 65C05: Monte Carlo methods 65C35: Stochastic particle methods [See also 82C80] 65C40: Computational Markov chains

Keywords
Berry–Esseen theorem Feyman–Kac models interacting particle systems

Citation

Del Moral, Pierre; Tindel, Samy. A Berry–Esseen theorem for Feynman–Kac and interacting particle models. Ann. Appl. Probab. 15 (2005), no. 1B, 941--962. doi:10.1214/105051604000000792. https://projecteuclid.org/euclid.aoap/1107271673


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References

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