Central limit theorem and moderate deviation principle for stochastic generalized Burgers-Huxley equation

In this work, we investigate the Central Limit Theorem (CLT) and Moderate Deviation Principle (MDP) for the solution of a stochastic generalized Burgers-Huxley (SGBH) equation with multiplicative Gaussian noise. The SGBH equation is a diffusion-convection-reaction type equation which consists of a nonlinearity of polynomial order, and we take into account 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 solution of SGBH equation. Using the weak convergence method, we establish the MDP and derive the corresponding rate function.