Ito's formula in UMD Banach spaces and regularity of solution of the Zakai equation

Journal article (2008)
Department
Delft Institute of Applied Mathematics (EEMCS) (TU Delft)
Copyright: © 2008 Brzezniak, Z.; Van Neerven; J.M.A.M.; Veraar, M.C.; Weis, L.; Elsevier
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Published Date

01-01-2008

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Source:

Journal of Differential Equations, 245, no. 1, p. 30-58, 2008

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Abstract

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Itô 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.

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