Stochastic Fractional Conservation Laws: Large deviation principle, Central limit theorem and Moderate deviation principle

TL;DR

This paper investigates stochastic fractional conservation laws, establishing large deviation principles, a central limit theorem, and moderate deviation principles using kinetic formulation, weak convergence, and doubling variables methods.

Contribution

It introduces new large deviation and limit theorems for stochastic fractional conservation laws within the kinetic framework, extending existing stochastic analysis techniques.

Findings

Established large deviation principle for stochastic fractional conservation laws.

Proved central limit theorem in the kinetic formulation setting.

Derived moderate deviation principle for the problem.

Abstract

In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence method and doubling variables method play a crucial role. As a consequence, we also establish moderate deviation principle for the underlying problem.