Fractional stochastic wave equation driven by a Gaussian noise rough in space

Jian Song; Xiaoming Song; Fangjun Xu

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arXiv · 1904.09905

Fractional stochastic wave equation driven by a Gaussian noise rough in space

Jian Song·Xiaoming Song·Fangjun Xu

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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 $H\in(\frac14, \frac12)$ 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 H\"older continuity in time and space variables for the solution.

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Jian Song, Xiaoming Song, Fangjun Xu. 2019-04-22. Fractional stochastic wave equation driven by a Gaussian noise rough in space. https://arxiv.org/abs/1904.09905

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