Poisson Stable Solutions for Stochastic Differential Equations with Lévy Noise  

作　　者：Xin LIU Zhen Xin LI 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第1期22-54,共33页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11522104,11871132 and 11925102);Xinghai Jieqing and DUT19TD14 funds from Dalian University of Technology。

摘　　要：In this paper,we use a unified framework to study Poisson stable(including stationary,periodic,quasi-periodic,almost periodic,almost automorphic,Birkhoff recurrent,almost recurrent in the sense of Bebutov,Levitan almost periodic,pseudo-periodic,pseudo-recurrent and Poisson stable)solutions for semilinear stochastic differential equations driven by infinite dimensional L′evy noise with large jumps.Under suitable conditions on drift,diffusion and jump coefficients,we prove that there exist solutions which inherit the Poisson stability of coefficients.Further we show that these solutions are globally asymptotically stable in square-mean sense.Finally,we illustrate our theoretical results by several examples.

关 键 词：Stochastic differential equation Lévy noise periodic solution quasi-periodic solution almost periodic solution Levitan almost periodic solution almost automorphic solution Birkhoff recurrent solution Poisson stable solution asymptotic stability 

分 类 号：O211.63[理学—概率论与数理统计]