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

TL;DR

This paper establishes L^p(p>2)-strong convergence for the slow component in two time-scale stochastic evolution equations driven by Lévy processes, advancing the stochastic averaging principle by handling jumps and higher moments.

Contribution

It introduces a novel approach to address the effects of Lévy jumps and higher moments in the stochastic averaging principle for two time-scale equations.

Findings

Proves L^p(p>2)-strong convergence of the slow component to the reduced equation.

Develops methods to handle Lévy process-induced jumps and higher order moments.

Provides conditions under which the averaging principle holds in this setting.

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.