On jumps stochastic slowly diffusion equations with fast oscillation coefficients

TL;DR

This paper establishes a large deviation principle for stochastic evolution equations with jumps, depending on two small parameters, highlighting the asymptotic behavior as the viscosity parameter diminishes faster than the homogenization parameter.

Contribution

It introduces a large deviation principle for stochastic equations with jumps involving two small parameters, with a focus on the asymptotic regime where viscosity diminishes faster than homogenization.

Findings

Large deviation principle in path-space for stochastic equations with jumps.

Uniform upper bound for the characteristic function of a Feller process.

Analysis of asymptotic behavior as viscosity parameter tends to zero faster than homogenization.

Abstract

We present a large deviation principle for some stochastic evolution equations with jumps which depend on two small parameters, when the viscosity parameter {\epsilon} tends to zero more quickly than the homogenization's one {\delta}{\epsilon} (written as a function of {\epsilon}). 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.