On extending classical filtering equations

Michael A. Kouritzin and Hongwei Long

Statistics & Probability Letters, 2008, vol. 78, issue 18, 3195-3202

Abstract: In this paper, we give a direct derivation of the Duncan-Mortensen-Zakai filtering equation, without assuming right continuity of the signal, nor its filtration, and without the usual finite energy condition. As a consequence, the Fujisaki-Kallianpur-Kunita equation is also derived. Our results can be applied to filtering problems in which the signal process has [alpha]-stable ([alpha]>1) components, and the sensor function is linear.

Date: 2008
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