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

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