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