Characterization of the optimal filter: the non markov case

Bhatt, Abhay G. ; Karandikar, Rajeeva L. (1999) Characterization of the optimal filter: the non markov case Stochastics and Stochastics Reports, 66 (3-4). pp. 177-204. ISSN 1045-1129

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We characterize the optimal filter in the nonlinear filtering theory as the unique solution to the Zakai equation. The results are very general as we allow the function h appearing in the filtering model to be discontinuous and unbounded. We consider the standard Markov model as well as the case when the signal X and the observation Y are solutions of a stochastic differential equation where the coefficients are allowed to depend on the past of Y. This is done via some results on existence of stationary solutions and solutions corresponding to certain measure valued evolution equations for controlled (and uncontrolled) martingale problems.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Group.
Keywords:Nonlinear Filtering; Zakai Equation; Martingale Problem; Controlled Martingale Problem; AMS Subject Classification 1991: Primary: 60G35; 62M20; 93E11; Secondary: 60G44; 60H15; 60J35
ID Code:73332
Deposited On:02 Dec 2011 08:38
Last Modified:02 Dec 2011 08:38

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