Some recent progress on stochastic heat equations
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Publication:2153091
DOI10.1007/s10473-019-0315-2zbMath1499.60220OpenAlexW2950571254MaRDI QIDQ2153091
Publication date: 1 July 2022
Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10473-019-0315-2
Gaussian noiseasymptotic behaviourHölder continuitychaos expansionhypercontractivitymoment boundsSkorohod integralTrotter-Lie formulajoint Hölder continuityFeynman-Kac formula for the moments of the solutionFeynman-Kac formula for the solutionGaussia random fieldstochastic partial differential equation (stochastic heat equation)
Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Initial value problems for second-order parabolic equations (35K15)
Related Items (14)
An improved characterisation of regular generalised functions of white noise and an application to singular SPDEs ⋮ Stochastic parabolic equations with singular potentials ⋮ The fractional stochastic heat equation driven by time-space white noise ⋮ Transportation cost-information inequality for a stochastic heat equation driven by fractional-colored noise ⋮ Almost surely time-space intermittency for the parabolic Anderson model with a log-correlated Gaussian field ⋮ The law of the iterated logarithm for spatial averages of the stochastic heat equation ⋮ BSDEs generated by fractional space-time noise and related SPDEs ⋮ Solvability of parabolic Anderson equation with fractional Gaussian noise ⋮ A large deviation principle for the stochastic heat equation with general rough noise ⋮ Decompositions of stochastic convolution driven by a white-fractional Gaussian noise ⋮ A splitting/polynomial chaos expansion approach for stochastic evolution equations ⋮ Asymptotics of the density of parabolic Anderson random fields ⋮ Stochastic heat equation with general rough noise ⋮ An integration by parts formula for stochastic heat equations with fractional noise
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