一类分数阶随机微分方程的均方渐近概周期解  

Square-Mean Asymptotically Almost Periodic Solutions for a Class of Fractional Stochastic Differential Equation

作　　者：姚慧丽 刘梦然 王晶囡 YAO Huili;LIU Mengran;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：《哈尔滨理工大学学报》2024年第1期150-158,共9页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11801122).

摘　　要：关于分数阶随机微分方程解的性质研究是近几年数学界的热门方向之一。针对Hilbert空间上一类线性分数阶随机微分方程,研究其均方渐近概周期温和解的存在性和唯一性,然后将这类线性分数阶随机微分方程的结论推广到对应的半线性分数阶随机微分方程中,利用Banach不动点定理讨论这类半线性分数阶随机微分方程均方渐近概周期温和解的存在唯一性,再利用Schauder不动点定理讨论这类方程在非Lipschitz条件下均方渐近概周期温和解的存在性。The study of the properties for fractional stochastic differential equation is one of the hot directions in the field of mathematics over the years.For a class of linear fractional stochastic differential equation on Hilbert space,the existence and uniqueness of its square-mean asymptotically almost periodic mild solutions are studied,and then the conclusions of this kind of linear fractional stochastic differential equation are extended to corresponding semi-linear fractional stochastic differential equation.The existence and uniqueness of square-mean asymptotically almost periodic mild solutions for this kind of semi-linear fractional stochastic differential equation are discussed by Banach fixed point theorem,and then discuss the existence of square-mean asymptotically almost periodic mild solutions by using Schauder fixed point theorem under non-Lipschitz conditions.

关 键 词：分数阶随机微分方程 均方渐近概周期解 BANACH不动点定理 SCHAUDER不动点定理 

分 类 号：O175.1[理学—数学]