This is an announcement for the paper "Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation" by Z. Brzezniak, J. M. A. M. van Neerven, M. C. Veraar and L. Weis.

Abstract: Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and time of the solutions of the Zakai equation.

Archive classification: math.PR math.FA

Mathematics Subject Classification: 60H15; 28C20; 35R60; 46B09; 60B11

Remarks: Accepted for publication in Journal of Differential Equations

The source file(s), zakai_01_04-2008_arxiv.tex: 83664 bytes, is(are) stored in gzipped form as 0804.0302.gz with size 25kb. The corresponding postcript file has gzipped size 148kb.

Submitted from: mark@profsonline.nl

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