Central limit theorem and moderate deviation principle for the stochastic generalized Burgers-Huxley equation with multiplicative noise

TL;DR

This paper studies the asymptotic behavior of solutions to the stochastic generalized Burgers-Huxley equation with multiplicative noise, proving a Central Limit Theorem and Moderate Deviation Principle using weak convergence methods.

Contribution

It establishes the CLT and MDP for the SGBH equation with infinite-dimensional noise, extending understanding of its probabilistic properties.

Findings

Proved the CLT for the SGBH equation solutions.

Established the MDP and derived the rate function.

Analyzed the convergence of the solution distribution.

Abstract

In this work, we investigate the Central Limit Theorem (CLT) and Moderate Deviation Principle (MDP) for the stochastic generalized Burgers-Huxley (SGBH) equation with multiplicative Gaussian noise. The SGBH equation is a diffusion-convection-reaction type equation which consists a nonlinearity of polynomial order, and we take into account of an infinite-dimensional noise having a coefficient that has linear growth. We first prove the CLT which allows us to establish the convergence of the distribution of the solution to a re-scaled SGBH equation to a desired distribution function. Furthermore, we extend our asymptotic analysis by investigating the MDP for the SGBH equation. Using the weak convergence method, we establish the MDP and derive the corresponding rate function.