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

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

2008-04-02

arxiv.org/abs/0804.0302v1

Mathematics

Probability

Accepted for publication in Journal of Differential Equations

Scientific paper

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.

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