Related papers: Stochastic wave equation with L\'evy white noise
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…
We consider the solution $\{u(t,x);t\geq0,x\in\mathbf{R}\}$ of a system of $d$ linear stochastic wave equations driven by a $d$-dimensional symmetric space-time L\'{e}vy noise. We provide a necessary and sufficient condition on the…
In this article, we consider a stochastic partial differential equation (SPDE) driven by a L\'evy white noise, with Lipschitz multiplicative term $\sigma$. We prove that under some conditions, this equation has a unique random field…
In this paper, we study the random field solution to the stochastic nonlinear wave equation (SNLW) with constant initial conditions and multiplicative noise $\sigma(u)\dot{L}$, where the nonlinearity is encoded in a Lipschitz function…
In this article, we study the stochastic wave equation in arbitrary spatial dimension $d$, with a multiplicative term of the form $\sigma(u)=u$, also known in the literature as the Hyperbolic Anderson Model. This equation is perturbed by a…
We examine the almost-sure asymptotics of the solution to the stochastic heat equation driven by a L\'evy space-time white noise. When a spatial point is fixed and time tends to infinity, we show that the solution develops unusually high…
We consider a 2D stochastic wave equation driven by a Gaussian noise, which is temporally white and spatially colored described by the Riesz kernel. Our first main result is the functional central limit theorem for the spatial average of…
In this paper, the successive approximation method is applied to investigate the existence and uniqueness of solutions to the stochastic differential equations (SDEs) driven by L\'evy noise under non-Lipschitz condition which is a much…
In this article, we introduce a L\'evy analogue of the spatially homogeneous Gaussian noise of Dalang (1999), and we construct a stochastic integral with respect to this noise. The spatial covariance of the noise is given by a tempered…
This paper deals with linear stochastic partial differential equations with variable coefficients driven by L\'{e}vy white noise. We first derive an existence theorem for integral transforms of L\'{e}vy white noise and prove the existence…
This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out by…
Martingale solutions of stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains, driven by the L\'evy noise consisting of the compensated time homogeneous Poisson random measure and the Wiener process are considered.…
In this article, we examine a stochastic partial differential equation (SPDE) driven by a symmetric $\alpha$-stable (S$\alpha$S) L\'evy noise, that is multiplied by a linear function $\sigma(u)=u$ of the solution. The solution is…
In this note, we establish a bi-parameter linear localization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing.
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4\textless{}H\textless{}1/2 in…
In this article we give sufficient and necessary conditions for the existence of a weak and mild solution to stochastic evolution equations with (general) L\'{e}vy noise taking values in the dual of a nuclear space. As part of our approach…
In this paper we study a class of stochastic partial differential equations in the whole space $\mathbb{R}^{d}$, with arbitrary dimension $d\geq 1$, driven by a Gaussian noise white in time and correlated in space. The differential operator…
We prove the local well-posedness of the periodic stochastic Korteweg-de Vries equation with the additive space-time white noise. In order to treat low regularity of the white noise in space, we consider the Cauchy problem in the Besov-type…
We consider the Navier-Stokes equations in vorticity form in $\mathbb{R}^2$ with a white noise forcing term of multiplicative type, whose spatial covariance is not regular enough to apply the It\^o calculus in $L^q$ spaces, $1<q<\infty$. We…
We investigate the moment asymptotics of the solution to the stochastic heat equation driven by a $(d+1)$-dimensional L\'evy space--time white noise. Unlike the case of Gaussian noise, the solution typically has no finite moments of order…