Large Deviation Principle for Semilinear Stochastic Evolution Equations with Monotone Nonlinearity and Multiplicative Noise

Hassan Dadashi-Arani, Bijan Z. Zangeneh

Published 2009-04-21, updated 2010-03-16Version 2

We demonstrate the large deviation property for the mild solutions of stochastic evolution equations with monotone nonlinearity and multiplica- tive noise. This is achieved using the recently developed weak convergence method, in studying the large deviation principle. An It^o-type inequality is a main tool in the proofs. We also give two examples to illustrate the applications of the theorems.