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inria-00410165, version 1

A Backward Particle Interpretation of Feynman-Kac Formulae

Pierre Del Moral () a, 1, 2, Arnaud Doucet () b, 3, Sumeetpal Singh () c, 4

N° RR-7019 (2009)

Résumé : We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals on-the-fly as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results w.r.t. the time horizon parameter as well as functional central limit theorems and exponential concentration estimates, yielding what seems to be the first results of this type for this class of models. We also illustrate these results in the context of computational physics and imaginary time Schroedinger type partial differential equations, with a special interest in the numerical approximation of the invariant measure associated to h-processes.

  • a –  INRIA
  • b –  University of British Columbia
  • c –  University of Cambridge
  • 1 :  Institut de Mathématiques de Bordeaux (IMB)
  • CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
  • 2 :  ALEA (INRIA Bordeaux - Sud-Ouest)
  • INRIA – Université de Bordeaux – CNRS : UMR5251
  • 3 :  Dept of Statistics & Dept of Computer Science
  • University of British Columbia
  • 4 :  Cavendish Laboratory - University of Cambridge
  • University of Cambridge
  • Domaine : Mathématiques/Probabilités
  • Mots-clés : Feynman-Kac models – mean field particle algorithms – functional central limit theorems – exponential concentration – non asymptotic estimates.
  • Référence interne : RR-7019
  • Versions disponibles :  v1 (18-08-2009) v2 (01-10-2009)
 
  • inria-00410165, version 1
  • http://hal.inria.fr/inria-00410165
  • oai:hal.inria.fr:inria-00410165
  • Contributeur : Pierre Del Moral <>
  • Soumis le : Mardi 18 Août 2009, 11:26:45
  • Dernière modification le : Mardi 18 Août 2009, 13:48:52