L^p(p>2)-strong convergence in stochastic averaging principle for two time-scales stochastic evolution equations driven by L\'evy process

Abstract

The main goal of the work is to study the stochastic averaging principle for two time-scales stochastic evolution equations driven by L\'evy process. The solution of reduced equation with modified coefficient is derived to approximate the slow component of original equation under suitable condition. It is shown that the slow component can strongly converge to the solution of corresponding reduced equation in L^p(p>2)-strong convergence sense.Our key and novelty is how to cope with the changes caused by L\'{e}vy process and higher order moments.