Related papers: Gaussian fluctuations for the wave equation under …
This paper consists of two parts. In the first part, we focus on the average of a functional over shifted Gaussian homogeneous noise and as the averaging domain covers the whole space, we establish a Breuer-Major type Gaussian fluctuation…
We consider a general class of SPDEs in $\mathbb{R}^d$ driven by a Gaussian spatially homogeneous noise which is white in time. We provide sufficient conditions on the coefficients and the spectral measure associated to the noise ensuring…
We give an introduction to the time-fractional stochastic heat equation driven by 1+d-parameter fractional time-space white noise, in the following two cases: (i) With additive noise (ii) With multiplicative noise. The fractional time…
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…
We determine the range of Hurst parameters that provide the necessary and sufficient conditions for the solvability, in $L^2(\Omega)$, of the stochastic wave equation: $ \frac{\partial^2 }{\partial t^2}u(t,x) =\Delta u(t,x)+\dot{W}(t,x)$,…
We consider the stochastic wave equation with multiplicative noise, which is fractional in time with index $H>1/2$, and has a homogeneous spatial covariance structure given by the Riesz kernel of order $\alpha$. The solution is interpreted…
In this article we present a {\it quantitative} central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the cases of space-time white noise and the white-colored noise…
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise…
We prove the existence and uniqueness of mild solution for the stochastic partial differential equation $$\left(\partial^\alpha - \textit{B} \right) u(t,x)= u(t,x) \cdot \dot{W}(t,x),$$ where $$\alpha \in (1/2, 1)\cup(1, 2);$$ $\textit{B}$…
We devise a stochastic Hamiltonian formulation of the water wave problem. This stochastic representation is built within the framework of the modelling under location uncertainty. Starting from restriction to the free surface of the general…
We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extending some recent work in [5]. The coefficients of our partial…
We study the bi-parameter local linearization of the one-dimensional nonlinear stochastic wave equation driven by a Gaussian noise, which is white in time and has a spatially homogeneous covariance structure of Riesz-kernel type. We…
For a sequence $\dot{L}^{\varepsilon}$ of L\'evy noises with variance $\sigma^2(\varepsilon)$, we prove the Gaussian approximation of the solution $u^{\varepsilon}$ to the stochastic wave equation driven by $\sigma^{-1}(\varepsilon)…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity…
This paper is devoted to investigating Freidlin-Wentzell's large deviation principle for one (spatial) dimensional nonlinear stochastic wave equation $\frac{\partial^2 u^{\e}(t,x)}{\partial t^2}=\frac{\partial^2 u^{\e}(t,x)}{\partial…
We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time and colored in space. Using Fourier analytic methods, we…
We consider stochastic nonlinear Schrodinger equations driven by an additive noise. The noise is fractional in time with Hurst parameter H in (0,1). It is also colored in space and the space correlation operator is assumed to be nuclear. We…
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…
We consider the linear stochastic wave equation driven by a Gaussian noise. We show that the solution satisfies a certain form of strong local nondeterminism and we use this property to derive the exact uniform modulus of continuity for the…