Related papers: Central limit theorems for stochastic wave equatio…
We prove a Central Limit Theorem for the linear statistics of two-dimensional Coulomb gases, with arbitrary inverse temperature and general confining potential, at the macroscopic and mesoscopic scales and possibly near the boundary of the…
The primary emphasis of this work is the development of a finite element based space-time discretization for solving the stochastic Lagrangian averaged Navier-Stokes (LANS-$\alpha$) equations of incompressible fluid turbulence with…
We consider Gaussian Laplace eigenfunctions on the two-dimensional flat torus (arithmetic random waves), and provide explicit Berry-Esseen bounds in the 1-Wasserstein distance for the normal and non-normal high-energy approximation of the…
We establish the stochastic comparison principles, including moment comparison principle as a special case, for solutions to the following nonlinear stochastic heat equation on $\mathbb{R}^d$ \[ \left(\frac{\partial }{\partial t}…
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 study a $d$-dimensional wave equation model ($2\leq d\leq 4$) with quadratic non-linearity and stochastic forcing given by a space-time fractional noise. Two different regimes are exhibited, depending on the Hurst parameter…
We consider the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In particular, we investigate the limiting behavior of solutions to SdNLW with regularized…
We prove the convergence of the solutions of the parabolic wave equation to that of the Gaussian white-noise model widely used in the physical literature. The random medium is isotropic and is assumed to have integrable correlation…
We prove a priori bounds for solutions of stochastic reaction diffusion equations with super-linear damping in the reaction term. These bounds provide a control on the supremum of solutions on any compact space-time set which only depends…
We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…
This paper studies the linear stochastic partial differential equation of fractional orders both in time and space variables $\left(\partial^\beta + \frac{\nu}{2} (-\Delta)^{\alpha/2} \right) u(t,x)= \lambda u(t,x) \dot{W}(t,x)$, where…
In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which…
We extend Walsh's theory of martingale measures in order to deal with hyperbolic stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation, and driven by spatially homogeneous…
We prove limit theorems for functionals of a Poisson point process using the Malliavin calculus on the Poisson space. The target distribution is conditionally either a Gaussian vector or a Poisson random variable. The convergence is stable…
In this paper, we prove existence, uniqueness and regularity for a class of stochastic partial differential equations with a fractional Laplacian driven by a space-time white noise in dimension one. The equation we consider may also include…
In this paper, we discuss an initial boundary value problem for the stochastic wave equation involving the nonlinear damping term $|u_t|^{q-2}u_t$ and a source term of the type $|u|^{p-2}u$. We firstly establish the local existence and…
We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients of our partial differential operator depend polynomially on the space…
Let $\mathcal{L}$ be the left-invariant distinguished Laplacian, and let $\mathrm{d}\rho$ denote the right Haar measure on a Damek--Ricci space $S$. Let $u(t,x)$ denote the solution to the wave equation $\partial_t^2 u-\mathcal{L} u=0$ with…
We introduce a model of Poisson random waves in $\mathbb{S}^{2}$ and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity.…