A Backward Particle Interpretation of Feynman-Kac Formulae

Pierre del Moral (1, 2) , Arnaud Doucet (3) , Sumeetpal Singh (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 ALEA - Advanced Learning Evolutionary Algorithms
3 Dept of Statistics & Dept of Computer Science
4 Cavendish Laboratory

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.

Mots clés: non asymptotic estimates; Feynman-Kac models; mean field particle algorithms; functional central limit theorems; exponential concentration; non asymptotic estimates.

Domaines: Probabilités [math.PR]

Pierre del Moral, Arnaud Doucet, Sumeetpal Singh. A Backward Particle Interpretation of Feynman-Kac Formulae. ESAIM: Mathematical Modelling and Numerical Analysis, 2010, 44 (5), pp.947-975. ⟨10.1051/m2an/2010048⟩. ⟨inria-00410165v2⟩