A basic identity for Kolmogorov operators in the space of continuous functions related to RDEs with multiplicative noise

DOI10.1214/13-AOP853zbMath1318.60068arXiv1212.5376OpenAlexW2015108784MaRDI QIDQ400560

Sandra Cerrai, Giuseppe Da Prato

Publication date: 22 August 2014

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.5376

zbMATH Keywords

Sobolev spacesPoincaré inequalityspectral gapstochastic reaction-diffusion equationsKolmogorov operators

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) PDEs on infinite-dimensional (e.g., function) spaces (= PDEs in infinitely many variables) (35R15)

Related Items (5)

Infinite-dimensional calculus under weak spatial regularity of the processes ⋮ Construction of a surface integral under local Malliavin assumptions, and related integration by parts formulas ⋮ Pathwise uniqueness for stochastic reaction-diffusion equations in Banach spaces with an Hölder drift component ⋮ \(L^2\)-theory for transition semigroups associated to dissipative systems ⋮ On generators of transition semigroups associated to semilinear stochastic partial differential equations

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• On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions
• Second order PDE's in finite and infinite dimension
• Stochastic Equations in Infinite Dimensions

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