Convergence of a Branching Particle Method to the Solution of the Zakai Equation

1998/10/01 by Dan Crisan, J. G. Gaines, Terry Lyons · 4 citations
Mathematics · Economics, Econometrics and Finance · Biochemistry, Genetics and Molecular Biology · #Stochastic processes and statistical mechanics #Stochastic processes and financial applications #Diffusion and Search Dynamics #Branching (polymer chemistry) #Randomness #Mathematics #Convergence (economics) #Sequence (biology) #Applied mathematics #Particle system #Weak convergence #Distribution (mathematics) #Statistical physics #Mathematical analysis #Computer science #Physics #Statistics

paper · doi:10.1137/s0036139996307371

openalex publication_date 1998/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

We construct a sequence of branching particle systems Un convergent in distribution to the solution of the Zakai equation. The algorithm based on this result can be used to solve numerically the filtering problem. The result is an improvement of the one presented in a recent paper [Crisan and T. Lyons, Prob. Theory Related Fields, 109 (1997), pp. 217--244], because it eliminates the extra degree of randomness introduced there.

Citations

• Nonlinear filtering and measure-valued processes
• Approximate Integration of Stochastic Differential Equations
• Novel approach to nonlinear/non-Gaussian Bayesian state estimation

Cited by

• Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems
• On the stability of interacting processes with applications to filtering and genetic algorithms
• A particle approximation of the solution of the Kushner–Stratonovitch equation
• Branching and interacting particle systems approximations of feynman-kac formulae with applications to non-linear filtering
• Monte Carlo method [wikipedia]