Annals of Probability

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

Abhay G. Bhatt, G. Kallianpur, and Rajeeva L. Karandikar

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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.

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

First available in Project Euclid: 19 April 2007

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Primary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11] 93E11: Filtering [See also 60G35] 60G44: Martingales with continuous parameter 60G57: Random measures 60H15: Stochastic partial differential equations [See also 35R60] 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Nonlinear filtering Zakai equation martingale problem robustness


Bhatt, Abhay G.; Kallianpur, G.; Karandikar, Rajeeva L. Uniqueness and Robustness of Solution of Measure-Valued Equations of Nonlinear Filtering. Ann. Probab. 23 (1995), no. 4, 1895--1938. doi:10.1214/aop/1176987808.

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