  In this work, we consider the stochastic Burgers-Huxley equation perturbed by
multiplicative Gaussian noise, and discuss about the global solvability results
and asymptotic behavior of solutions. We show the existence of a global strong
solution of the stochastic Burgers-Huxley equation, by making use of a local
monotonicity property of the linear and nonlinear operators and a stochastic
generalization of localized version of the Minty-Browder technique. We then
discuss about the inviscid limit of the stochastic Burgers-Huxley equation to
Burgers as well as Huxley equations. By considering the noise to be additive
Gaussian, Exponential estimates for exit from a ball of radius $R$ by time $T$
for solutions of the stochastic Burgers-Huxley equation is derived, and then
studied in the context of Freidlin-Wentzell type large deviations principle.
Finally, we establish the existence of a unique ergodic and strongly mixing
invariant measure for the stochastic Burgers-Huxley equation with additive
Gaussian noise, using the exponential stability of solutions.
