Diffusion limit for the radiative transfer equation perturbed by a Markovian process

TL;DR

This paper investigates the stochastic diffusive limit of a non-linear kinetic radiative transfer equation perturbed by a Markovian process, demonstrating convergence to a stochastic non-linear fluid limit under suitable scaling.

Contribution

It extends the perturbed test-functions method to analyze the stochastic diffusive limit of a non-linear radiative transfer equation with Markovian perturbations.

Findings

Proves convergence in law to a stochastic non-linear fluid limit.

Generalizes the perturbed test-functions method for stochastic kinetic equations.

Provides a rigorous mathematical framework for stochastic radiative transfer limits.

Abstract

We study the stochastic diffusive limit of a kinetic radiative transfer equation, which is non-linear, involving a small parameter and perturbed by a smooth random term. Under an appropriate scaling for the small parameter, using a generalization of the perturbed test-functions method, we show the convergence in law to a stochastic non-linear fluid limit.