A backward particle interpretation of Feynman-Kac formulae
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) no. 5, pp. 947-975.

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.

DOI : https://doi.org/10.1051/m2an/2010048
Classification : 65C05,  65C35,  60G35,  47D08
Mots clés : Feynman-Kac models, mean field particle algorithms, functional central limit theorems, exponential concentration, non asymptotic estimates
     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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {947--975},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {5},
     year = {2010},
     doi = {10.1051/m2an/2010048},
     mrnumber = {2731399},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2010048/}
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 - Modélisation Mathématique et Analyse Numérique
PY  - 2010
DA  - 2010///
SP  - 947
EP  - 975
VL  - 44
IS  - 5
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/m2an/2010048/
UR  - https://www.ams.org/mathscinet-getitem?mr=2731399
UR  - https://doi.org/10.1051/m2an/2010048
DO  - 10.1051/m2an/2010048
LA  - en
ID  - M2AN_2010__44_5_947_0
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Del Moral, Pierre; Doucet, Arnaud; Singh, Sumeetpal S. A backward particle interpretation of Feynman-Kac formulae. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) no. 5, pp. 947-975. doi : 10.1051/m2an/2010048. http://www.numdam.org/articles/10.1051/m2an/2010048/

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