【摘要】 研究一类随机微分方程无限时间的跟踪性.首先给出了Ito型随机微分方程在均方意义下无限时间(ω,δ)-伪轨与无限时间(ω,ε)-跟踪的定义,其次证明了一个修正的Schauder不动点定理,最后用Malliavin导数证明了Ito随机微分方程的无限时间跟踪的存在性定理.推广确定的微分方程的跟踪性到随机情形,结论表明:在由Ito随机微分方程生成的随机动力系统中,依然存在无限时间的跟踪.更多还原

【Abstract】 This paper focuses on the infinite time shadowing of a class of stochastic differential equations(SDEs). Firstly, the definitions of(ω,δ)-pseudo orbit and(ω,ε)-shadowing of infinite time in mean square sense are presented. Then the modified Schauder’s fixed point theorem is proved.Lastly, the theorem about the existence of infinite time shadowing of Ito SDEs is proved by Malliavin derivative. The shadowing of the deterministic differential equations is extended to the stochastic case,and the result shows the fact that infinite time shadowing is still a character in random dynamical systems generated by Ito SDEs.更多还原