Stochastic heat equation with general rough noise

DOI10.1214/21-AIHP1161zbMath1483.60094OpenAlexW4210686825MaRDI QIDQ2078021

Xiong Wang, Yaozhong Hu

Publication date: 25 February 2022

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

Full work available at URL: https://doi.org/10.1214/21-aihp1161

zbMATH Keywords

weak solutionstrong solutionweighted spacespathwise uniquenessadditive noisemajorizing measurerough Gaussian noise(nonlinear) stochastic heat equationHölder constants over unbounded domaintemporal and spatial asymptotic growthweighted heat kernel estimates

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Heat kernel (35K08)

Related Items (4)

Nonlinear stochastic wave equation driven by rough noise ⋮ Global well-posedness for the nonlinear generalized parabolic Anderson model equation ⋮ A large deviation principle for the stochastic heat equation with general rough noise ⋮ Quantitative central limit theorems for the parabolic Anderson model driven by colored noises

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noise
• On the chaotic character of the stochastic heat equation. II
• On the chaotic character of the stochastic heat equation, before the onset of intermitttency
• Stochastic heat equation with rough dependence in space
• Integration questions related to fractional Brownian motion
• Parabolic Anderson model with rough dependence in space
• Some recent progress on stochastic heat equations
• Asymptotic separation for stochastic Volterra integral equations with doubly singular kernels
• Spatial asymptotics for the parabolic Anderson model driven by a Gaussian rough noise
• The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities
• SPDEs with affine multiplicative fractional noise in space with index \(\frac{1}{4} < H < \frac{1}{2}\)
• Fourier Analysis and Nonlinear Partial Differential Equations
• Stochastic Equations in Infinite Dimensions
• Upper and Lower Bounds for Stochastic Processes

This page was built for publication: Stochastic heat equation with general rough noise