The Annals of Applied Probability

Genealogies and Increasing Propagation of Chaos For Feynman-Kac and Genetic Models

L. Miclo and P. Del Moral

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Abstract

A path-valued interacting particle systems model for the genealogical structure of genetic algorithms is presented. We connect the historical process and the distribution of the whole ancestral tree with a class of Feynman-Kac formulae on path space. We also prove increasing and uniform versions of propagation of chaos for appropriate particle block size and time horizon yielding what seems to be the first result of this type for this class of particle systems.

Article information

Source
Ann. Appl. Probab., Volume 11, Number 4 (2001), 1166-1198.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1015345399

Digital Object Identifier
doi:10.1214/aoap/1015345399

Mathematical Reviews number (MathSciNet)
MR1878294

Zentralblatt MATH identifier
1040.60031

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J05: Discrete-time Markov processes on general state spaces 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx] 93E11: Filtering [See also 60G35]

Keywords
Interacting particle systems genetic algorithms historical process genealogy relative entropy propagation of chaos non linear filtering Feynman-Kac formula empirical processes

Citation

Moral, P. Del; Miclo, L. Genealogies and Increasing Propagation of Chaos For Feynman-Kac and Genetic Models. Ann. Appl. Probab. 11 (2001), no. 4, 1166--1198. doi:10.1214/aoap/1015345399. https://projecteuclid.org/euclid.aoap/1015345399


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References

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