Strong Averaging Principle For A Class Of Slow-fast Singular SPDEs Driven By α-stable Processes

In this paper,the strong averaging principle is researched for a class of slow-fast SPDEs driven by α-stable process.Using Zvonkin’s transformation and classical Khasminkii time discretization method to prove that when the drift coefficient is only Holder continuous,the solution of the slow equation Xε can strongly converges to the solution of its corresponding averaging equation X,that isTo do this,we study the well-posedness of the fast-slow system,give a priori estimations of(Xε,Yε),construct an auxiliary process(Xtε,Ytε).Secondly,Zvonkin transformation method and Khasminkii time discretization method are introduced to prove the main results.Finally,as applications,an example is also provided to explain our result.The result of this paper is brand new.