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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 filtering of hidden Markov models, as well as in 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.
@article{M2AN_2010__44_5_947_0,
author = {Del Moral, Pierre and Doucet, Arnaud and Singh, Sumeetpal S.},
title = {A backward particle interpretation of {Feynman-Kac} formulae},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {947--975},
publisher = {EDP-Sciences},
volume = {44},
number = {5},
year = {2010},
doi = {10.1051/m2an/2010048},
mrnumber = {2731399},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010048/}
}
TY - JOUR AU - Del Moral, Pierre AU - Doucet, Arnaud AU - Singh, Sumeetpal S. TI - A backward particle interpretation of Feynman-Kac formulae JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2010 SP - 947 EP - 975 VL - 44 IS - 5 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010048/ DO - 10.1051/m2an/2010048 LA - en ID - M2AN_2010__44_5_947_0 ER -
%0 Journal Article %A Del Moral, Pierre %A Doucet, Arnaud %A Singh, Sumeetpal S. %T A backward particle interpretation of Feynman-Kac formulae %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2010 %P 947-975 %V 44 %N 5 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010048/ %R 10.1051/m2an/2010048 %G en %F M2AN_2010__44_5_947_0
Del Moral, Pierre; Doucet, Arnaud; Singh, Sumeetpal S. A backward particle interpretation of Feynman-Kac formulae. ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue on Probabilistic methods and their applications, Tome 44 (2010) no. 5, pp. 947-975. doi: 10.1051/m2an/2010048
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