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∈(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.
Original language | English |
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Pages (from-to) | 4561-4616 |
Number of pages | 56 |
Journal | Annals of Probability |
Volume | 45 |
Issue number | 6B |
DOIs | |
Publication status | Published - 12 Dec 2017 |
Keywords
- Stochastic heat equation
- fractional Brownian motion
- Feynman–Kac formula
- Wiener chaos expansion
- intermittency Citation