一类非自治随机微分方程的均方渐近概周期解  

SQUARE-MEAN ASYMPTOTICALLY ALMOST PERIODIC SOLUTION ON A CLASS OF NONAUTONOMOUS STOCHASTIC DIFFERENTIAL EQUATIONS

作　　者：姚慧丽[1] 王健伟[1] 

机构地区：[1]哈尔滨理工大学应用科学学院数学系,黑龙江哈尔滨150080

出　　处：《数学杂志》2016年第2期319-327,共9页Journal of Mathematics

基　　金：黑龙江省教育厅科学技术研究项目(12511110)

摘　　要：本文研究了一类在可分Hilbert空间中的非自治随机微分方程的均方渐近概周期解.利用"Acquistapace-Terreni"条件,开方族和Banach不动点原理讨论了该类随机微分方程的均方渐近概周期解的存在唯一性,推广了该类随机微分方程的均方概周期解的存在唯一性问题.In this papre, the square-mean asymptotically almost periodic solution is studied on a class of nonautonomous stochastic differential equations in a separable Hilbert space. By using the ＂Acquistapace-Terreni＂conditions, evolution families and Banach fixed point theorem,the existence and uniqueness of square-mean asymptotically almost periodic solution on this kind of nonautonomous stochastic differential equations are discussed. The problems on the existence and uniqueness of square-mean almost periodic solutions on this kind of equation are generalized.

关 键 词：均方渐近概周期解 非自治随机微分方程 Banach不动点原理 

分 类 号：O211.63[理学—概率论与数理统计]