On homogenization of space-time dependent and degenerate random flows II

TL;DR

This paper investigates the long-term behavior of diffusions in complex, degenerate random media with space-time dependencies, extending previous invariance principles to non-critical scalings.

Contribution

It generalizes the invariance principle for diffusions in random media to include non-critical space-time scalings, accommodating degeneracies in the diffusion coefficients.

Findings

Established invariance principles for non-critical scalings.

Extended homogenization results to degenerate, space-time dependent diffusions.

Provided a framework for analyzing long-term behavior in complex random environments.

Abstract

We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle is proved for the critical rescaling of the diffusion. Here, we generalize this approach to diffusions whose space-time scaling differs from the critical one.