Electronic Journal of Probability

On a Class of Discrete Generation Interacting Particle Systems

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

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1461097646

Digital Object Identifier
doi:10.1214/EJP.v6-89

Mathematical Reviews number (MathSciNet)
MR1873293

Zentralblatt MATH identifier
0991.60017

Subjects
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

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


Export citation

References

  • D. Blount and M.A. Kouritzin, Rates for branching particle approximations of continuous-discrete filters, (in preparation), 1999.
  • D. Crisan and P. Del Moral and T.J. Lyons, Non linear filtering using branching and interacting particle systems, Markov Processes and Related Fields, 5 (3): 293-319, 1999.
  • P. Del Moral, Measure valued processes and interacting particle systems. Application to non linear filtering problems, The Annals of Applied Probability, 8 (2):438-495, 1998.
  • P. Del Moral, Non linear filtering: interacting particle solution, Markov Processes and Related Fields, 2 (4):555-581, 1996.
  • P. Del Moral and L. Miclo, Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non Linear Filtering, In J. Azéma and M. Emery and M. Ledoux and M. Yor, Séminare de Probabilités XXXIV, Lecture Notes in Mathematics, Vol. 1729, pages 1-145. Springer-Verlag, 2000.
  • R.L. Dobrushin, Central limit theorem for nonstationary Markov chains, I, Theor. Prob. Appl., 1, 66-80, 1956.
  • R.L. Dobrushin, Central limit theorem for nonstationary Markov chains, II, Theor. Prob. Appl., 1, 330-385, 1956.
  • J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes. A Series of Comprehensive Studies in Mathematics 288. Springer-Verlag, 1987.
  • T. Shiga and H. Tanaka, Central limit theorem for a system of Markovian particles with mean field interaction, Zeitschrift für Wahrscheinlichkeitstheorie verwandte Gebiete, 69, 439-459, 1985.
  • A.N. Shiryaev, Probability. Number 95 in Graduate Texts in Mathematics. Springer-Verlag, New-York, Second Edition, 1996.