# A backward particle interpretation of Feynman-Kac formulae

Pierre Del Moral; Arnaud Doucet; Sumeetpal S. Singh

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 44, Issue: 5, page 947-975
- ISSN: 0764-583X

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topDel Moral, Pierre, Doucet, Arnaud, and Singh, Sumeetpal S.. "A backward particle interpretation of Feynman-Kac formulae." ESAIM: Mathematical Modelling and Numerical Analysis 44.5 (2010): 947-975. <http://eudml.org/doc/250778>.

@article{DelMoral2010,

abstract = {
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.
},

author = {Del Moral, Pierre, Doucet, Arnaud, Singh, Sumeetpal S.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Feynman-Kac models; mean field particle algorithms; functional
central limit theorems; exponential concentration; non asymptotic estimates; functional central limit theorems; convergence filtering; hidden Markov models; Schrödinger equations; numerical example},

language = {eng},

month = {8},

number = {5},

pages = {947-975},

publisher = {EDP Sciences},

title = {A backward particle interpretation of Feynman-Kac formulae},

url = {http://eudml.org/doc/250778},

volume = {44},

year = {2010},

}

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

DA - 2010/8//

PB - EDP Sciences

VL - 44

IS - 5

SP - 947

EP - 975

AB -
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.

LA - eng

KW - Feynman-Kac models; mean field particle algorithms; functional
central limit theorems; exponential concentration; non asymptotic estimates; functional central limit theorems; convergence filtering; hidden Markov models; Schrödinger equations; numerical example

UR - http://eudml.org/doc/250778

ER -

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