Related papers: Stochastic homogenization of $L^\infty$ variationa…
In this paper, we investigate ergodicity in total variation of the process $X_t$, related to a L\'evy-driven stochastic differential equation with unbounded coefficients, and describe the speed of convergence to the respective invariant…
We study the stochastic homogenization and obtain a random fluctuation theory for semilinear elliptic equations with a rapidly varying random potential. To first order, the effective potential is the average potential and the nonlinearity…
We study the ergodic behaviour of a discrete-time process $X$ which is a Markov chain in a stationary random environment. The laws of $X_t$ are shown to converge to a limiting law in (weighted) total variation distance as $t\to\infty$.…
We study suspensions of solid particles in a viscous incompressible fluid in the presence of highly oscillatory velocity-dependent surface forces. The flow at a small Reynolds number is modeled by the Stokes equations coupled with the…
We investigate the homogenization of inclusions of infinite conductivity, randomly stationary distributed inside a homogeneous conducting medium. A now classical result by Zhikov shows that, under a logarithmic moment bound on the…
We consider an elliptic equation with purely imaginary, highly heterogeneous, and large random potential with a sufficiently rapidly decaying correlation function. We show that its solution is well approximated by the solution to a…
This paper investigates the convergence of density approximations for stochastic heat equation in both uniform convergence topology and total variation distance. The convergence order of the densities in uniform convergence topology is…
In this paper we study the randomized heat equation with homogeneous boundary conditions. The diffusion coeffcient is assumed to be a random variable and the initial condition is treated as a stochastic process. The solution of this…
For a homogenization problem associated to a linear elliptic operator, we prove the existence of a distributional corrector and we find an approximation scheme for the homogenized coefficients. We also study the convergence rates in the…
We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…
This article establishes an algebraic error estimate for the stochastic homogenization of fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media. The approach is similar to that of Armstrong and Smart in…
This work develops a quantitative homogenization theory for random suspensions of rigid particles in a steady Stokes flow, and completes recent qualitative results. More precisely, we establish a large-scale regularity theory for this…
We prove homogenization for a class of nonconvex (possibly degenerate) viscous Hamilton-Jacobi equations in stationary ergodic random environments in one space dimension. The results concern Hamiltonians of the form $G(p)+V(x,\omega)$,…
In this paper, we study the stochastic-periodic homogenization of Non-stationary Navier-Stokes Type Equations on anisotropic heterogeneous media. More precisely, we are interested in the stochastic-periodic homogenization of its variational…
This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the…
We study homogenization it its most basic form $$-\left(a\left(\frac{x}{\varepsilon}\right) u_{\varepsilon}'(x)\right)' = f(x) \quad \mbox{for} ~x \in (0,1),$$ where $a(\cdot)$ is a positive $1-$periodic continuous function, $f$ is smooth…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…
We prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation result, which we believe is of some interest too.
Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly…