Strong Propagations of Chaos in Moran's Type Particle Interpretations of Feynman–Kac Measures

Abstract

This article is concerned with strong propagations of chaos properties in Moran's type particle interpretations of continuous time Feynman–Kac formulae. These particle schemes can also be seen as approximating models of simple generalized spatially homogeneous Boltzmann equations. We provide a simple and original semigroup analysis based on empirical tensor measures combinatorics properties, martingales techniques, and coupling arguments. We also design a general and abstract framework without any topological assumption on the state space. This yields a natural way to analyze the propagations of chaos properties for interacting particle models on path space. Applications to genealogical type particle algorithms for the nonlinear filtering and smoothing problem are also discussed.

Keywords:

• Feynman–Kac formulae
• Genealogical particle algorithms
• Particle systems
• Path-valued Markov processes
• Propagation of chaos

Mathematics Subject Classification:

• Primary 60J25
• Secondary 60J75, 60K35, 60F25, 60F05