## The Annals of Probability

### Stochastic heat equation with rough dependence in space

#### 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 $H\in (\frac{1}{4},\frac{1}{2})$ 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 $\sigma(0)=0$.

#### Article information

Source
Ann. Probab., Volume 45, Number 6B (2017), 4561-4616.

Dates
Revised: December 2016
First available in Project Euclid: 12 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aop/1513069267

Digital Object Identifier
doi:10.1214/16-AOP1172

Mathematical Reviews number (MathSciNet)
MR3737918

Zentralblatt MATH identifier
06838127

#### Citation

Hu, Yaozhong; Huang, Jingyu; Lê, Khoa; Nualart, David; Tindel, Samy. Stochastic heat equation with rough dependence in space. Ann. Probab. 45 (2017), no. 6B, 4561--4616. doi:10.1214/16-AOP1172. https://projecteuclid.org/euclid.aop/1513069267

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