On a Class of Discrete Generation Interacting Particle Systems

P. Del Moral (Univ. P. Sabatier)
M. A. Kouritzin (University of Alberta)
L. Miclo (Univ. P. Sabatier)


The asymptotic behavior of a general class of discrete generation interacting particle systems is discussed. We provide Lp-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.

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Pages: 1-26

Publication Date: May 16, 2001

DOI: 10.1214/EJP.v6-89


  1. D. Blount and M.A. Kouritzin, Rates for branching particle approximations of continuous-discrete filters, (in preparation), 1999. Math. Reviews number not avilable
  2. 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. Math. Review 2000f:93087
  3. 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. Math. Review 99c:60213
  4. P. Del Moral, Non linear filtering: interacting particle solution, Markov Processes and Related Fields, 2 (4):555-581, 1996. Math. Review 97k:60175
  5. P. Del Moral and L. Miclo, Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non Linear Filtering, In J. AzÈma and M. Emery and M. Ledoux and M. Yor, Séminare de ProbabilitÈs XXXIV, Lecture Notes in Mathematics, Vol. 1729, pages 1-145. Springer-Verlag, 2000. Math. Review 2001g:60091
  6. R.L. Dobrushin, Central limit theorem for nonstationary Markov chains, I, Theor. Prob. Appl., 1, 66-80, 1956. Math. Review 19,184h
  7. R.L. Dobrushin, Central limit theorem for nonstationary Markov chains, II, Theor. Prob. Appl., 1, 330-385, 1956. Math. Review 20 #3592
  8. J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes. A Series of Comprehensive Studies in Mathematics 288. Springer-Verlag, 1987. Math. Review 89k:60044
  9. T. Shiga and H. Tanaka, Central limit theorem for a system of Markovian particles with mean field interaction, Zeitschrift f¸r Wahrscheinlichkeitstheorie verwandte Gebiete, 69, 439-459, 1985. Math. Review 88a:60056
  10. A.N. Shiryaev, Probability. Number 95 in Graduate Texts in Mathematics. Springer-Verlag, New-York, Second Edition, 1996. Math. Review 97c:60003

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