Large Deviation Principle for Mild Solutions of Stochastic Evolution Equations with Multiplicative Lévy Noise
arXiv:1309.1935
Abstract
We demonstrate the large deviation principle in the small noise limit for the mild solution of stochastic evolution equations with monotone nonlinearity. A recently developed method, weak convergent method, has been employed in studying the large deviations. we have used essentially the main result of Budhiraja et al., [4] which discloses the variational representation of exponential integrals w.r.t. the Lévy noise. An Itô-type inequality is a main tool in our proofs. Our framework covers a wide range of semilinear parabolic, hyperbolic and delay differential equations. We give some examples to illustrate the applications of the results.
28 pages. arXiv admin note: text overlap with arXiv:0904.3305 by other authors