Abstract
Ever since the technique of the Kalman-Bucy filter was popularized, there has been an intense interest in finding new classes of finite-dimensional recursive filters. In the late seventies, the concept of the estimation algebra of a filtering system was introduced. It has been the major tool in studying the Duncan-Mortensen-Zakai equation. Recently the second author has constructed general finite-dimensional filters which contain both Kalman-Bucy filters and Benes filter as special cases. In this paper we consider a filtering system with arbitrary nonlinear driftf(x) which satisfies some regularity assumption at infinity. This is a natural assumption in view of Theorem 10 of [DTWY] in a special case. Under the assumption on the observation h(x)=constant, we propose writing down the solution of the Duncan-Mortensen-Zakai equation explicitly.
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Communicated by S. K. Mitter
This research was supported by Army Grant DAAH-04-93G-0006.
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Yau, S.T., Yau, S.S.T. Explicit solution of a Kolmogorov equation. Appl Math Optim 34, 231–266 (1996). https://doi.org/10.1007/BF01182625
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DOI: https://doi.org/10.1007/BF01182625