About strong propagation of chaos for interacting particle approximations of Feynman-Kac formulae

Pierre del Moral (1) , Laurent Miclo (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

Recently we have introduced Moran type interacting particle systems in order to numerically compute normalized continuous time Feynman-Kac formulae. These schemes can also be seen as approximating procedures for certain simple generalized spatially homogeneous Boltzmann equations, so strong propagation of chaos is known to hold for them. We will give a new proof of this result by studying the evolution of tensorized empirical measures and then applying two straightforward coupling arguments. The only difficulty is in the first step to find nice martingales, and this will be done via the introduction of another family of Moran semigroups. This work also procures us the opportunity to present an appropriate abstract setting, in particular without any topological assumption on the state space, and to apply a genealogical algorithm for the smoothing problem in nonlinear filtering context.

Mots clés: genealogical processes and smoothing problems in nonlinear filtering; Feynman-Kac formulae; perturbations of general Markov processes by jump bounded generators; interacting particle systems; weak and strong propagation of chaos; tensorized empirical measures; Moran semigroups and martingales; coupling; genealogical processes and smoothing problems in nonlinear filtering.

Domaines: Probabilités [math.PR]

Pierre del Moral, Laurent Miclo. About strong propagation of chaos for interacting particle approximations of Feynman-Kac formulae. Stoch. Anal. Appl., 2007, 25 (3), pp.519-575. ⟨hal-00021658⟩