Transportation Cost-Information Inequality for Stochastic Wave Equation
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DOI: 10.1007/s10440-019-00292-y
Abstract: In this paper, we prove a Talagrand’s \(T_{2}\) transportation cost-information inequality for the law of stochastic wave equation in spatial dimension \(d=3\) driven by the Gaussian random field, white in time and correlated in space,… read more here.
Keywords: cost information; transportation cost; information inequality; stochastic wave ... See more keywords
Random attractors for non-autonomous stochastic wave equations with nonlinear damping and white noise
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DOI: 10.1186/s13662-020-02664-3
Abstract: This paper is concerned with the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with additive white noise, for which the nonlinear damping has a critical cubic growth rate. By showing the pullback… read more here.
Keywords: autonomous stochastic; non autonomous; nonlinear damping; stochastic wave ... See more keywords
Can the stochastic wave equation with strong drift hit zero?
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DOI: 10.1214/19-ejp279
Abstract: We study the stochastic wave equation with multiplicative noise and singular drift: \[ \partial_tu(t,x)=\Delta u(t,x)+u^{-\alpha}(t,x)+g(u(t,x))\dot{W}(t,x) \] where $x$ lies in the circle $\mathbf{R}/J\mathbf{Z}$ and $u(0,x)>0$. We show that (i) If $0 read more here.
Keywords: stochastic wave; wave equation; drift; equation strong ... See more keywords
Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
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DOI: 10.1214/19-ejp363
Abstract: In this article, we consider the stochastic wave equation on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally integrable functions $\gamma$… read more here.
Keywords: space; space time; equation; stochastic wave ... See more keywords