A nonasymptotic theorem for unnormalized Feynman–Kac particle models

F. Cérou; P. Del Moral; A. Guyader

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 3, page 629-649
  • ISSN: 0246-0203

Abstract

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We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first results of this type for this class of unnormalized models. We also illustrate these results in the context of particle absorption models, with a special interest in rare event analysis.

How to cite

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Cérou, F., Del Moral, P., and Guyader, A.. "A nonasymptotic theorem for unnormalized Feynman–Kac particle models." Annales de l'I.H.P. Probabilités et statistiques 47.3 (2011): 629-649. <http://eudml.org/doc/243964>.

@article{Cérou2011,
abstract = {We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first results of this type for this class of unnormalized models. We also illustrate these results in the context of particle absorption models, with a special interest in rare event analysis.},
author = {Cérou, F., Del Moral, P., Guyader, A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {interacting particle systems; Feynman–Kac semigroups; nonasymptotic estimates; genetic algorithms; Boltzmann–Gibbs measures; Monte Carlo models; rare events; Feynman-Kac semigroups; Boltzmann-Gibbs measures},
language = {eng},
number = {3},
pages = {629-649},
publisher = {Gauthier-Villars},
title = {A nonasymptotic theorem for unnormalized Feynman–Kac particle models},
url = {http://eudml.org/doc/243964},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Cérou, F.
AU - Del Moral, P.
AU - Guyader, A.
TI - A nonasymptotic theorem for unnormalized Feynman–Kac particle models
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 3
SP - 629
EP - 649
AB - We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first results of this type for this class of unnormalized models. We also illustrate these results in the context of particle absorption models, with a special interest in rare event analysis.
LA - eng
KW - interacting particle systems; Feynman–Kac semigroups; nonasymptotic estimates; genetic algorithms; Boltzmann–Gibbs measures; Monte Carlo models; rare events; Feynman-Kac semigroups; Boltzmann-Gibbs measures
UR - http://eudml.org/doc/243964
ER -

References

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  3. [3] F. Cerou and A. Guyader. Adaptive multilevel splitting for rare event analysis. Stoch. Anal. Appl. 25 (2007) 417–433. Zbl1220.65009MR2303095
  4. [4] T. Dean and P. Dupuis. Splitting for rare event simulation: A large deviations approach to design and analysis. Stochastic Process. Appl. 119 (2009) 562–587. Zbl1157.60019MR2494004
  5. [5] P. Del Moral. Feynman–Kac Formulae. Genealogical and Interacting Particle Systems. Springer, New York, 2004. Zbl1130.60003MR2044973
  6. [6] P. Del Moral, A. Doucet and A. Jasra. Sequential Monte Carlo samplers. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 (2006) 411–436. Zbl1105.62034MR2278333
  7. [7] P. Del Moral, A. Doucet and G. W. Peters. Sharp propagations of chaos estimates for Feynman–Kac particle models. Theory Probab. Appl. 51 (2007) 459–485. Zbl1156.60072MR2325545
  8. [8] P. Del Moral, F. Patras and S. Rubenthaler. Coalescent tree based functional representations for some Feynman–Kac particle models. Ann. Appl. Probab. 19 (2009) 778–825. Zbl1189.60171MR2521888
  9. [9] A. Doucet, N. de Freitas and N. Gordon, eds. Sequential Monte Carlo Methods in Practice. Springer, New York, 2001. Zbl1056.93576MR1847783
  10. [10] A. M. Johansen, P. Del Moral and A. Doucet. Sequential Monte Carlo samplers for rare events. In Proceedings of 6th International Workshop on Rare Event Simulation. Bamberg, Germany, 2006. 
  11. [11] A. Lagnoux. Rare event simulation. Probab. Engrg. Inform. Sci. 20 (2006) 45–66. Zbl1101.65005MR2187629

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