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

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JournalJournal of Differential Equations
DatePublished - 1 Jul 2008
Issue number1
Volume245
Number of pages29
Pages (from-to)30-58
Original languageEnglish

Abstract

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an M 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. (C) 2008 Elsevier Inc. All rights reserved.

    Research areas

  • stochastic integration in Banach spaces, UMD spaces, Ito formula, stochastic evolution equations, Zakai equation, non-autonomous equations, Wong-Zakai approximation, PARTIAL-DIFFERENTIAL EQUATIONS, STOCHASTIC INTEGRATION, EVOLUTION-EQUATIONS, VALUES

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