Stochastic heat equation with rough dependence in space

Hu, Yaozhong
Huang, Jingyu
Lê, Khoa
Nualart, David
Tindel, Samy

Publication date

May 2015

Publisher

HAL CCSD

Abstract

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 1/4<H<1/2 in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient is differentiable with a Lipschitz derivative and vanishes at 0. In the case of a multiplicative noise, that is the linear equation, we derive the Wiener chaos expansion of the solution and a Feynman-Kac formula for the moments of the solution. These results allow us to establish sharp lower and upper asymptotic bounds for the moments of the solution

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Stochastic heat equation with rough dependence in space

Abstract

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Stochastic heat equation with rough dependence in space

Abstract

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