Related papers: Stochastic homogenization of Gaussian fields on ra…

We consider the linear stochastic wave equation with spatially homogenous Gaussian noise, which is fractional in time with index $H>1/2$. We show that the necessary and sufficient condition for the existence of the solution is a relaxation…

We consider a nonlinear stochastic heat equation on $[0,T]\times [-L,L]$, driven by a space-time white noise $W$, with a given initial condition $u_0: \mathbb{R} \to \mathbb{R}$ and three different types of (vanishing) boundary conditions:…

This paper studies quantitative homogenization of elliptic equations with random, uniformly elliptic coefficients that vanish in a union of random holes. Assuming an upper bound on the size of the holes and a separation condition between…

In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…

We study a non-relativistic charged particle on the Euclidean plane R^2 subject to a perpendicular constant magnetic field and an R^2-homogeneous random potential in the approximation that the corresponding random Landau Hamiltonian on the…

Homogenization for non-local operators in periodic environments has been studied intensively. So far, these works are mainly devoted to the qualitative results, that is, to determine explicitly the operators in the limit. To the best of…

For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of…

We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…

Let $M$ be a compact, connected Riemannian manifold whose Riemannian volume measure is denoted by $\sigma$. Let $f: M \rightarrow \mathbb{R}$ be a non-constant eigenfunction of the Laplacian. The random wave conjecture suggests that in…

The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is…

The stochastic partial differential equation (SPDE) approach is widely used for modeling large spatial datasets. It is based on representing a Gaussian random field $u$ on $\mathbb{R}^d$ as the solution of an elliptic SPDE $L^\beta u =…

We show homogenization for a family of $\mathbb{R}^d$-valued stable-like processes $(X_t^{\epsilon;\theta})_{t\ge 0}$, $\epsilon\in(0,1]$, whose (random) Fourier symbols equal…

In this paper we study the Hamiltonian dynamics of charged particles subject to a non-self-consistent stochastic electric field, when the plasma is in the so-called weak turbulent regime. We show that the asymptotic limit of the Vlasov…

The aim of our work is to provide a simple homogenization and discrete-to-continuum procedure for energy driven problems involving stochastic rapidly-oscillating coefficients. Our intention is to extend the periodic unfolding method to the…

The mean field limit of large-population symmetric stochastic differential games is derived in a general setting, with and without common noise, on a finite time horizon. Minimal assumptions are imposed on equilibrium strategies, which may…

Skew-symmetric functions are a class of functions defined on a product space $M \times M$ that are antisymmetric with respect to the order of their inputs. In [13], the authors proved that non-deterministic skew-symmetric Gaussian fields…

Spatially inhomogeneous functions, which may be smooth in some regions and rough in other regions, are modelled naturally in a Bayesian manner using so-called Besov priors which are given by random wavelet expansions with…

We prove that diffusion equations with a space-time stationary and ergodic, divergence-free drift homogenize in law to a deterministic stochastic partial differential equation with Stratonovich transport noise. In the absence of spatial…

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…

In stochastic homogenization of elliptic equations, the corrector plays a central role. Under a finite range of dependence assumption on the coefficient field, we show that the large-scale spatial averages of the corrector approach those of…