Parabolic Anderson model with rough or critical Gaussian noise

DOI10.1214/18-AIHP904zbMath1475.60113MaRDI QIDQ2320389

Xia Chen

Publication date: 22 August 2019

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.aihp/1557820837

zbMATH Keywords

fractionalBrownian motionparabolic Anderson equationFeynman-Kac's representationmoment asymptoticsDalang's conditionrough and critical Gaussian noises

Mathematics Subject Classification ID

Brownian motion (60J65) Large deviations (60F10) White noise theory (60H40) (n)-body potential quantum scattering theory (81U10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (15)

Space-time fractional Anderson model driven by Gaussian noise rough in space ⋮ Exact asymptotics of the stochastic wave equation with time-independent noise ⋮ Parabolic Anderson model with a fractional Gaussian noise that is rough in time ⋮ Moment bounds for a generalized Anderson model with Gaussian noise rough in space ⋮ Moment intermittency in the PAM with asymptotically singular noise ⋮ Interpolating the stochastic heat and wave equations with time-independent noise: solvability and exact asymptotics ⋮ Parabolic Anderson model with rough noise in space and rough initial conditions ⋮ Exponential asymptotics for Brownian self-intersection local times under Dalang's condition ⋮ Solvability of parabolic Anderson equation with fractional Gaussian noise ⋮ Fractional stochastic wave equation driven by a Gaussian noise rough in space ⋮ Precise high moment asymptotics for parabolic Anderson model with log-correlated Gaussian field ⋮ Stochastic comparisons for stochastic heat equation ⋮ Moment estimates for some renormalized parabolic Anderson models ⋮ Spatial asymptotics for the Feynman-Kac formulas driven by time-dependent and space-fractional rough Gaussian fields with the measure-valued initial data ⋮ A \(K\)-rough path above the space-time fractional Brownian motion

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