Open Access
November 2017 Stochastic heat equation with rough dependence in space
Yaozhong Hu, Jingyu Huang, Khoa Lê, David Nualart, Samy Tindel
Ann. Probab. 45(6B): 4561-4616 (November 2017). DOI: 10.1214/16-AOP1172


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 $H\in (\frac{1}{4},\frac{1}{2})$ in the space variable. The existence and uniqueness of the solution $u$ are proved assuming the nonlinear coefficient $\sigma(u)$ is differentiable with a Lipschitz derivative and $\sigma(0)=0$.


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Yaozhong Hu. Jingyu Huang. Khoa Lê. David Nualart. Samy Tindel. "Stochastic heat equation with rough dependence in space." Ann. Probab. 45 (6B) 4561 - 4616, November 2017.


Received: 1 May 2015; Revised: 1 December 2016; Published: November 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06838127
MathSciNet: MR3737918
Digital Object Identifier: 10.1214/16-AOP1172

Primary: 60G15 , 60H07 , 60H10 , 65C30

Keywords: Feynman–Kac formula , fractional Brownian motion , Intermittency , Stochastic heat equation , Wiener chaos expansion

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 6B • November 2017
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