On jumps stochastic slowly diffusion equations with fast oscillation coefficients

Abstract

We present a large deviation principle for some stochastic evolution equations with jumps which depend on two small parameters, when the viscosity parameter ε tends to zero more quickly than the homogenization's one δε (written as a function of ε). In particular, we highlighted a large deviation principle in path-space using some classical techniques and a uniform upper bound for the characteristic function of a Feller process.