Electronic Journal of Probability

On a Class of Discrete Generation Interacting Particle Systems

P. Del Moral, M. Kouritzin, and L. Miclo

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The asymptotic behavior of a general class of discrete generation interacting particle systems is discussed. We provide $L_p$-mean error estimates for their empirical measure on path space and present sufficient conditions for uniform convergence of the particle density profiles with respect to the time parameter. Several examples including mean field particle models, genetic schemes and McKean's Maxwellian gases will also be given. In the context of Feynman-Kac type limiting distributions we also prove central limit theorems and we start a variance comparison for two generic particle approximating models.

Article information

Electron. J. Probab., Volume 6 (2001), paper no. 16, 26 pp.

Accepted: 16 May 2001
First available in Project Euclid: 19 April 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 93E11: Filtering [See also 60G35] 62L20: Stochastic approximation

Interacting particle systems genetic algorithms Feynman-Kac formulas stochastic approximations central limit theorem

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Del Moral, P.; Kouritzin, M.; Miclo, L. On a Class of Discrete Generation Interacting Particle Systems. Electron. J. Probab. 6 (2001), paper no. 16, 26 pp. doi:10.1214/EJP.v6-89. https://projecteuclid.org/euclid.ejp/1461097646

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