Diffusion Approximation for Transport Equations with Dissipative Drifts for Time Dependent Coefficients

TL;DR

This paper extends classical diffusion approximation results to time-dependent dissipative drifts, demonstrating convergence of diffusions with multiplicative noise to dynamical systems and solving related transport equations.

Contribution

It generalizes existing diffusion approximation theory to include time-dependent dissipative drifts, providing new convergence results and solutions for associated transport equations.

Findings

Diffusions with multiplicative noise converge to dynamical systems as diffusivity tends to zero.

The paper derives solutions to transport equations linked to these diffusions.

It broadens the applicability of diffusion approximation to time-dependent settings.

Abstract

We consider a generalization of classical results of Freidlin and Wentzell to the case of time dependent dissipative drifts. We show the convergence of diffusions with multiplicative noise in the zero limit of a diffusivity parameter to the related dynamical systems. The solution to the associated transport equation is obtained as an application.