## Annals of Probability

### Uniqueness and Robustness of Solution of Measure-Valued Equations of Nonlinear Filtering

#### Abstract

We consider the Zakai equation for the unnormalized conditional distribution $\sigma$ when the signal process $X$ takes values in a complete separable metric space $E$ and when $h$ is a continuous, possibly unbounded function on $E$. It is assumed that $X$ is a Markov process which is characterized via a martingale problem for an operator $A_0$. Uniqueness of solution for the measure-valued Zakai and Fujisaki-Kallianpur-Kunita equations is proved when the test functions belong to the domain of $A_0$. It is also shown that the conditional distributions are robust.

#### Article information

Source
Ann. Probab., Volume 23, Number 4 (1995), 1895-1938.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176987808

Digital Object Identifier
doi:10.1214/aop/1176987808

Mathematical Reviews number (MathSciNet)
MR1379173

Zentralblatt MATH identifier
0861.60051

JSTOR