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

TL;DR

This paper rigorously derives a stochastic nonlinear diffusion equation from a radiative transfer equation with random noise, using Hilbert expansions to handle the stochastic perturbations.

Contribution

It introduces a novel rigorous derivation of a stochastic diffusion limit for radiative transfer equations perturbed by Wiener noise, employing advanced expansion techniques.

Findings

Successful derivation of the stochastic diffusion equation

Use of third-order Hilbert expansion to manage noise complexities

Establishment of convergence proof for the stochastic limit

Abstract

The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the convergence relies on a formal Hilbert expansion and the estimation of the remainder. The Hilbert expansion has to be done up to order 3 to overcome some diffculties caused by the random noise.