一类随机积分微分方程的均方渐近概周期解  

Square-mean asymptotically almost periodic solutions for a kind of stochastic integro-differential equations

作　　者：姚慧丽 刘梦然 霍贵珍 王晶囡 YAO Huili;LIU Mengran;HUO Guizhen;WANG Jingnan(College of Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2022年第4期394-401,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11801122)。

摘　　要：在实可分的Hilbert空间考虑一类随机积分微分方程的均方渐近概周期解的存在唯一性问题。基于Banach压缩映射原理和随机分析技巧,给出了此方程存在唯一均方渐近概周期解的一组充分条件。研究表明,如果方程预解算子族指数稳定,在适当的条件下,方程存在唯一均方渐近概周期解。The problem of the existence and uniqueness of square-mean asymptotically almost periodic solutions is considered for a kind of stochastic integro-differential equations in a real separable Hilbert space.Based on Banach contraction mapping principle and the stochastic analysis techniques,a set of sufficient conditions for the existence and uniqueness of square-mean asymptotically almost periodic solutions are given for the considered equation.It is shown that if the resolvent operators of equation are exponentially stable,then there is a unique square-mean asymptotically almost periodic solution of the equation under proper conditions.

关 键 词：随机积分微分方程 均方渐近概周期解 存在性 唯一性 BANACH压缩映射原理 

分 类 号：Q939.97[生物学—微生物学]