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.
Citation
Abhay G. Bhatt. G. Kallianpur. Rajeeva L. Karandikar. "Uniqueness and Robustness of Solution of Measure-Valued Equations of Nonlinear Filtering." Ann. Probab. 23 (4) 1895 - 1938, October, 1995. https://doi.org/10.1214/aop/1176987808
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