A CLT for degenerate diffusions with periodic coefficients, and application to homogenisation of linear PDEs

TL;DR

This paper establishes a functional central limit theorem for degenerate diffusions with periodic coefficients and applies it to the homogenization of certain linear PDEs, extending classical results to degenerate cases.

Contribution

It generalizes the classical CLT for diffusions to include degenerate cases with periodic coefficients and applies this to homogenize linear PDEs.

Findings

Proves a functional CLT for degenerate diffusions with periodic coefficients.

Demonstrates homogenization results for linear degenerate elliptic and parabolic PDEs.

Extends classical diffusion results to broader degenerate settings.

Abstract

In this article, we obtain a functional CLT for a class of degenerate diffusion processes with periodic coefficients, thus generalizing the already classical results in the context of uniformly elliptic diffusions. As an application, we also discuss periodic homogenization of a class of linear degenerate elliptic and parabolic PDEs.