Large Deviation Principle for Occupation Measures of Stochastic Generalized Burgers–Huxley Equation

The present work deals with the global solvability as well asymptotic analysis of stochastic generalized Burgers–Huxley (SGBH) equation perturbed by a white-in-time and correlated-in-space noise defined in bounded interval $${\mathbb {R}}$$ . We first prove existence unique mild strong solution to SGBH then obtain an invariant measure. Later, we establish two major properties Markovian semigroup associated solutions equation, that is, irreducibility Feller property. These guarantee uniqueness measures ergodicity also. Then, under further assumptions on coefficient, discuss ergodic behavior providing large deviation principle for occupation measure time (Donsker–Varadhan), which describes exact rate exponential convergence.