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 $\sigma(0)=0$.
Citation
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. https://doi.org/10.1214/16-AOP1172
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