A relative compactness criterion in Wiener-Sobolev spaces and application to semi-linear stochastic PDEs

DOI10.1016/S0022-1236(03)00236-2zbMath1055.60051MaRDI QIDQ1876250

Vlad Bally, Bruno Saussereau

Publication date: 16 August 2004

Published in: Journal of Functional Analysis (Search for Journal in Brave)

zbMATH Keywords

weak solutionMalliavin calculusstochastic partial differential equationsWiener chaoscompactness criterionbackward doubly stochastic differental equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) PDEs with low regular coefficients and/or low regular data (35R05) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (10)

Relatively compact criteria for Hilbert valued random fields on abstract Wiener space ⋮ Anticipating random periodic solutions. I: SDEs with multiplicative linear noise. ⋮ Relatively compact families of functionals on abstract Wiener space and applications ⋮ Stability in mean of partial variables for stochastic reaction diffusion systems ⋮ Random periodic solutions of SPDEs via integral equations and Wiener-Sobolev compact embedding ⋮ SPDEs with polynomial growth coefficients and the Malliavin calculus method ⋮ A remark on the mean square distance between the solutions of fractional SDEs and Brownian SDEs ⋮ Theory and application of stability for stochastic reaction diffusion systems ⋮ Pathwise random periodic solutions of stochastic differential equations ⋮ Backward doubly stochastic differential equations with polynomial growth coefficients

Cites Work

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• The Malliavin calculus
• Backward doubly stochastic differential equations and systems of quasilinear SPDEs
• Pathwise stochastic Taylor expansions and stochastic viscosity solutions for fully nonlinear stochastic PDEs
• Stochastic viscosity solutions for nonlinear stochastic partial differential equations. II.
• Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations
• Weak solutions for SPDE's and backward doubly stochastic differential equations

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