On the necessary and sufficient conditions to solve a heat equation with general additive Gaussian noise

DOI10.1007/s10473-019-0304-5zbMath1499.60222arXiv1803.07885OpenAlexW2963713621MaRDI QIDQ2153079

Samy Tindel, Yanghui Liu, Yaozhong Hu

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://arxiv.org/abs/1803.07885

zbMATH Keywords

Besov spaceHölder continuitystochastic heat equationsufficient and necessary conditionWong-Zakai approximationpathwise solution\(L^2\) solutiongeneral Gaussian noise

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic calculus of variations and the Malliavin calculus (60H07) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (2)

Some recent progress on stochastic heat equations ⋮ Solvability of parabolic Anderson equation with fractional Gaussian noise

Cites Work

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• Spatial asymptotics for the parabolic Anderson models with generalized time-space Gaussian noise
• On a modelled rough heat equation
• Solving the KPZ equation
• Feynman-Kac formula for the heat equation driven by fractional noise with Hurst parameter \(H < 1/2\)
• A theory of regularity structures
• Feynman-Kac formula for heat equation driven by fractional white noise
• Stochastic heat equation with rough dependence in space
• Stochastic heat equation driven by fractional noise and local time
• Intermittence and nonlinear parabolic stochastic partial differential equations
• Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E's
• Forward, backward and symmetric stochastic integration
• Stochastic evolution equations with a spatially homogeneous Wiener process
• Global well-posedness of the dynamic \(\Phi^{4}\) model in the plane
• \(m\)-order integrals and generalized Itô's formula; the case of a fractional Brownian motion with any Hurst index
• Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency
• Sample paths of the solution to the fractional-colored stochastic heat equation
• Fourier Analysis and Nonlinear Partial Differential Equations
• The Malliavin Calculus and Related Topics
• Elements of Stochastic Calculus via Regularization
• Stochastic Equations in Infinite Dimensions

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