A new numerical scheme for the Zakaï equation

Abstract

The aim of this paper is to propose a new method for numerical approximations of the solution of the linear stochastic partial differential equation arising in non-linear filtering problems: the Zakaï equation. The approximation scheme is based on a representation of the solution of the Zakaï equation involving a stochastic part arising from the observation process and a deterministic partial differential equation in which are involved only the parameters of the signal process. We may then employ a dynamic programming principle in order to write down an approximation of this partial differential equation. A quantization method based on the underlying diffusion process (which is a not the signal itself) is used.

This paper has been withdrawn by the author due to a crucial gap in Proposition 1