Strong averaging principle for slow-fast SPDEs with Poisson random measures

Abstract

This work concerns the problem associated with an averaging principle fortwo-time-scales stochastic partial differential equations (SPDEs) drivenby cylindrical Wiener processes and Poisson random measures. Under suitabledissipativity conditions, the existence of an averaging equation eliminatingthe fast variable for the coupled system is proved, and as a consequence,the system can be reduced to a single SPDE with a modified coefficient.Moreover, it is shown that the slow component mean-square strongly convergesto the solution of the corresponding averaging equation.