A new proof for the convergence of Picard's filter using partial Malliavin calculus

Abstract

The discrete-time approximation for nonlinear filtering problems is related to both of strong and weak approximations of stochastic differential equations. In this paper, we propose a new method of proof for the convergence of approximate nonlinear filter analyzed by Jean Picard (1984), and show a more general result than the original one. For the proof, we develop an analysis of Hilbert space valued functionals on Wiener space.

15 pages

References in corpus (2)

• Weak approximation of stochastic differential equations and application to derivative pricing
• A duality approach for the weak approximation of stochastic differential equations

Cited by in corpus (1)

• A high order time discretization of the solution of the non-linear filtering problem