Stochastic heat equation with rough dependence in space
Research output: Contribution to journal › Article › peer-review
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.
|Number of pages||56|
|Journal||Annals of Probability|
|Publication status||Published - 12 Dec 2017|
- Stochastic heat equation, fractional Brownian motion, Feynman–Kac formula, Wiener chaos expansion, intermittency Citation