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

TY - JOUR

T1 - Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation

AU - Brzezniak, Z.

AU - van Neerven, J. M. A. M.

AU - Veraar, M. C.

AU - Weis, L.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - 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.

AB - 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.

KW - stochastic integration in Banach spaces

KW - UMD spaces

KW - Ito formula

KW - stochastic evolution equations

KW - Zakai equation

KW - non-autonomous equations

KW - Wong-Zakai approximation

KW - PARTIAL-DIFFERENTIAL EQUATIONS

KW - STOCHASTIC INTEGRATION

KW - EVOLUTION-EQUATIONS

KW - VALUES

UR - http://www.scopus.com/inward/record.url?scp=43049114149&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2008.03.026

DO - 10.1016/j.jde.2008.03.026

M3 - Article

SN - 0022-0396

VL - 245

SP - 30

EP - 58

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -