A Backward Particle Interpretation of Feynman-Kac Formulae
DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
DEL MORAL, Pierre
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Language
en
Article de revue
This item was published in
ESAIM: Mathematical Modelling and Numerical Analysis. 2010, vol. 44, n° 5, p. 947-975
EDP Sciences
English 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. ...Read more >
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.Read less <
English Keywords
non asymptotic estimates
Feynman-Kac models
mean field particle algorithms
functional central limit theorems
exponential concentration
non asymptotic estimates.
ANR Project
Sécurité et fiabilité des techniques de tatouages - ANR-06-SETI-0009
Origin
Hal imported