Evolution equations for Markov processes: application to the white-noise theory of filtering

Bhatt, A. G. ; Karandikar, R. L. (1995) Evolution equations for Markov processes: application to the white-noise theory of filtering Applied Mathematics and Optimization, 31 (3). pp. 327-348. ISSN 0095-4616

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Official URL: http://www.springerlink.com/content/n366q810r67m04...

Related URL: http://dx.doi.org/10.1007/BF01215995

Abstract

Let X be a Markov process taking values in a complete, separable metric spaceE and characterized via a martingale problem for an operator A. We develop a criterion for invariant measures when range A is a subset of continuous functions on E. Using this, uniqueness in the class of all positive finite measures of solutions to a (perturbed) measure-valued evolution equation is proved when the test functions are taken from the domain of A. As a consequence, it is shown that in the characterization of the optimal filter (in the white-noise theory of filtering) as the unique solution to an analogue of Zakai (as well as Fujisaki-Kallianpur-Kunita) equation, it suffices to take domain A as the class of test functions where the signal process is the solution to the martingale problem for A.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Markov Process; Martingale Problem; Invariant Measure; Evolution Equation
ID Code:73318
Deposited On:02 Dec 2011 10:31
Last Modified:02 Dec 2011 10:31

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