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November 2020 Fractional stochastic wave equation driven by a Gaussian noise rough in space
Jian Song, Xiaoming Song, Fangjun Xu
Bernoulli 26(4): 2699-2726 (November 2020). DOI: 10.3150/20-BEJ1204

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.

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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

Received: 1 April 2019; Published: November 2020
First available in Project Euclid: 27 August 2020

zbMATH: 07256157
MathSciNet: MR4140526
Digital Object Identifier: 10.3150/20-BEJ1204

Keywords: fractional Brownian motion , Hölder continuity , Intermittency , Malliavin calculus , Skorohod integral , Stochastic wave equation

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 4 • November 2020
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