Related papers: Central limit theorems for stochastic wave equatio…
In this article, we study the stochastic wave equation in spatial dimensions $d \le 2$ with multiplicative L\'evy noise that can have infinite $p$-th moments. Using the past light-cone property of the wave equation, we prove the existence…
We consider a stochastic wave equation in space dimension three driven by a noise white in time and with an absolutely continuous correlation measure given by the product of a smooth function and a Riesz kernel. Let $p_{t,x}(y)$ be the…
In this paper we consider a general class of second order stochastic partial differential equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and it has a homogeneous spatial covariance. Using the techniques of…
Let $\{u(t,x)\}_{t>0,x\in{{\mathbb R}^{d}}}$ denote the solution to the linear (fractional) stochastic heat equation. We establish rates of convergence with respect to the uniform distance between the density of spatial averages of solution…
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity…
We consider stochastic partial differential equations on $\mathbb{R}^{d}, d\geq 1$, driven by a Gaussian noise white in time and colored in space, for which the pathwise uniqueness holds. By using the Skorokhod representation theorem we…
We consider the family of stochastic partial differential equations indexed by a parameter $\eps\in(0,1]$, \begin{equation*} Lu^{\eps}(t,x) = \eps\sigma(u^\eps(t,x))\dot{F}(t,x)+b(u^\eps(t,x)), \end{equation*} $(t,x)\in(0,T]\times\Rd$ with…
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 paper, we consider the dynamics of integrable stochastic Hamiltonian systems. Utilizing the Nagaev-Guivarc'h method, we obtain several generalized results of the central limit theorem. Making use of this technique and the Birkhoff…
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…
In this paper, we consider a system of $k$ second order non-linear stochastic partial differential equations with spatial dimension $d \geq 1$, driven by a $q$-dimensional Gaussian noise, which is white in time and with some spatially…
Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
In this paper we consider a system of non-linear stochastic heat equations on $\mathbb{R}^d$ driven by a Gaussian noise which is white in time and has a homogeneous spatial covariance. Under some suitable regularity and non degeneracy…
We consider a $d$-dimensional random field $u=(u(x), x\in D)$ that solves a system of elliptic stochastic equations on a bounded domain $D\subset \mathbb{R}^k$, with additive white noise and spatial dimension $k=1,2,3$. Properties of $u$…
In the pathwise stochastic calculus framework, the paper deals with the general study of equations driven by an additive Gaussian noise, with a drift function having an infinite limit at point zero. An ergodic theorem and the convergence of…
This paper is concerned with a wave equation in dimension $d\in \{1,2, 3\}$, with a multiplicative space-time Gaussian noise which is fractional in time and homogeneous in space. We provide necessary and sufficient conditions on the…
The wave speed of a stochastic wave equation driven by Riesz noise on the unbounded multidimensional spatial domain is estimated based on discrete measurements. Central limit theorems for second-order variations of the observations in…
Let $\left(u(t,x), t\geq 0, x\in \mathbb{R}^d\right)$ be the solution to the stochastic heat or wave equation driven by a Gaussian noise which is white in time and white or correlated with respect to the spatial variable. We consider the…
Motivated by the task of computing normalizing constants and importance sampling in high dimensions, we study the dimension dependence of fluctuations for additive functionals of time-inhomogeneous Langevin-type diffusions on…
We analyze the generalized $k$-variations for the solution to the wave equation driven by an additive Gaussian noise which behaves as a fractional Brownian with Hurst parameter $H>\frac{1}{2}$ in time and which is white in space. The…