Central limit theorem and moderate deviation principle for stochastic scalar conservation laws

TL;DR

This paper proves a central limit theorem and a moderate deviation principle for stochastic scalar conservation laws using kinetic solutions, addressing the challenges posed by the absence of viscous terms.

Contribution

It introduces a novel analysis framework for stochastic conservation laws without viscous terms, employing weak convergence and doubling variables methods.

Findings

Established a central limit theorem for stochastic scalar conservation laws.

Proved a moderate deviation principle in the kinetic solution framework.

Addressed the challenges of non-viscous stochastic PDEs.

Abstract

We establish a central limit theorem and prove a moderate deviation principle for stochastic scalar conservation laws. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and doubling variables method play a key role.