Abstract
In this article, we consider fractional stochastic wave equations on $\mathbb{R}$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in(\frac{1}{4},\frac{1}{2})$ in space. We prove the existence and uniqueness of the mild Skorohod solution, establish lower and upper bounds for the $p$th moment of the solution for all $p\ge2$, and obtain the Hölder continuity in time and space variables for the solution.
Citation
Jian Song. Xiaoming Song. Fangjun Xu. "Fractional stochastic wave equation driven by a Gaussian noise rough in space." Bernoulli 26 (4) 2699 - 2726, November 2020. https://doi.org/10.3150/20-BEJ1204
Information