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Nonlinear stochastic wave Equation driven by rough noise (2110.13800v1)
Published 26 Oct 2021 in math.PR and math.AP
Abstract: In this paper, we obtain the existence and uniqueness of the strong solution to one spatial dimension stochastic wave equation $\frac{\partial2 u(t,x)}{\partial t2}=\frac{\partial2 u(t,x)}{\partial x2}+\sigma(t,x,u(t,x))\dot{W}(t,x)$ assuming $\sigma(t,x,0)=0$, where $\dot W$ is a mean zero Gaussian noise which is white in time and fractional in space with Hurst parameter $H\in(1/4, 1/2)$.