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

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 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.

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