A Moran particle system approximation of Feynman–Kac formulae

• Published in: Stochastic processes and their applications Vol. 86; no. 2; pp. 193 - 216
• Main Authors: Moral, P.Del, Miclo, L.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-04-2000; Elsevier Science; Elsevier
• Series: Stochastic Processes and their Applications
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; Global analysis, analysis on manifolds; Inference from stochastic processes; time series analysis; Mathematics; Measure valued dynamical systems defined by Feynman–Kac formulae; Modelling and identification; Nonlinear filtering; Probability and statistics; Probability theory and stochastic processes; Quantitative weak propagation of chaos; Sciences and techniques of general use; Statistics; Stochastic processes; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Weighted sampling Moran processes; Weighted sampling Moran processes Measure valued dynamical systems defined by Feynman-Kac formulae Quantitative weak propagation of chaos Nonlinear filtering; Quantitative weak propagation of chaos; Weighted sampling Moran processes; Nonlinear filtering; Measure valued dynamical systems defined by Feynman–Kac formulae; Chaos; Markov process; Filtering; Weighted sampling; Dynamical system; Laplacian; Brownian motion; Riemann manifold; Particle system; Chaos propagation; Moran process; Feynman Kac formula; Diffusion; Sampling; Regularity
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/S0304-4149(99)00094-0

We present a weighted sampling Moran particle system model for the numerical solving of a class of Feynman–Kac formulae which arise in different fields. Our major motivation was from nonlinear filtering, but our approach is context free. We will show that under certain regularity conditions the resulting interacting particle scheme converges to the considered nonlinear equations. In the setting of nonlinear filtering, the
L
1
-convergence exponent resulting from our proof also improves recent results on other particle interpretations of these equations.