Large deviation principle for semilinear stochastic evolution equations with Poisson noise

Abstract

We demonstrate the large deviation principle in the small noise limit for the mild solution of semilinear stochastic evolution equations with monotone nonlinearity and multiplicative Poisson noise. A recently developed method in studying the large deviation principle, weak convergent method, is employed. We apply the result obtained by Budhiraja et al.,7 that reveals the variational representation of exponential integrals w.r.t. the Poisson random measure. Our framework covers a wide range of parabolic, hyperbolic and functional differential equations. We give some examples to illustrate the applications of our results.