Related papers: On homogenization of space-time dependent and dege…

We study a diffusion process with random space-time dependent coefficients. Moreover the diffusion matrix is allowed to degenerate. An invariance principle is proved provided that the diffusion coefficient is controlled by a time…

The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the…

We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…

We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…

Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…

This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…

The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of…

Diffusion processes are studied theoretically for the case where the diffusion coefficient is itself a time and position dependent random function. We investigate how inhomogeneities and fluctuations of the diffusion coefficient affect the…

Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…

Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic…

We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…

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 consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the…

The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…

The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…

We consider a diffusion process with coefficients that are periodic outside of an 'interface region' of finite thickness. The question investigated in the articles [1,2] is the limiting long time / large scale behaviour of such a process…

We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…

We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…