Stochastic heat equation with rough dependence in space

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Colleges, School and Institutes


This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H∈(¼,½) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient σ(u) is differentiable with a Lipschitz derivative and σ(0)=0.


Original languageEnglish
Pages (from-to)4561-4616
Number of pages56
JournalAnnals of Probability
Issue number6B
Publication statusPublished - 12 Dec 2017


  • Stochastic heat equation, fractional Brownian motion, Feynman–Kac formula, Wiener chaos expansion, intermittency Citation