The mild and weak solutions of a stochastic parabolic Anderson equation

DOI10.1016/j.jmaa.2014.09.056zbMath1301.60079OpenAlexW1967682457MaRDI QIDQ472298

Lijun Miao

Publication date: 19 November 2014

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.09.056

zbMATH Keywords

weak solutionBrownian motionmild solutionGaussian potential

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for second-order parabolic equations (35K15)

Related Items (2)

Hölder continuity for parabolic Anderson equation with non-Gaussian noise ⋮ Feynman–Kac formula for parabolic Anderson model in Gaussian potential and fractional white noise

Cites Work

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• Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related parabolic Anderson models
• Brownian motion and parabolic Anderson model in a renormalized Poisson potential
• Feynman-Kac formula for heat equation driven by fractional white noise
• Spectral representations of infinitely divisible processes
• Confinement of Brownian motion among Poissonian obstacles in \(\mathbb{R}^d, d\geq 3\)
• Brownian asymptotics in a Poissonian environment
• Moment asymptotics for the continuous parabolic Anderson model.
• Almost sure asymptotics for the continuous parabolic Anderson model
• Localization for Schrödinger operators with Poisson random potential
• Almost-sure exponential behavior of a stochastic anderson model with continuous space parameter
• Stochastic Calculus
• Mild solution to parabolic Anderson model in Gaussian and Poisson potential
• Stochastic Equations in Infinite Dimensions

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