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

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.

Accepted for publication in Journal of Differential Equations

Cited by in corpus (1)

• Stochastic integration in UMD Banach spaces