Un théorème d'unicité pour l'equation de zakaï

Abstract

We prove, under rather general conditions, that the conditional density in nonlinear filtering is the unique solution-within an appropriate space of processes-of Zakai's equation. The main restriction is that all coefficients are supposed to be bounded.

Nonlinear filtering of Itô-Lévy stochastic differential equations with continuous observations

“…This has been done in the case of finite dimensional signal using techniques from p.d.e. theory (see Baras, Blankenship and Hopkins [2], Sheu [21], Chaleyat-Maurel, Michel and Pardoux [6], Rozovskii [20], Bensoussan [4]) and using martingale problems (see Hijab [8], Kurtz and Ocone [12], Bhatt, Kalliapur and Karandikar [3]). Nonlinear filtering of stochastic PDEs is developed in Sritharan and Hobbs [23] and Sritharan [24].…”