一类随机微分方程的均方渐近概周期温和解  

Square-Mean Asymptotically Almost Periodic Mild Solutions for a Class of Stochastic Differential Equations

作　　者：姚慧丽 张悦娇 YAO Hui-li;ZHANG Yue-jiao(School of Applied Sciences,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学应用科学学院

出　　处：《哈尔滨理工大学学报》2019年第4期143-148,共6页Journal of Harbin University of Science and Technology

基　　金：黑龙江省教育厅2011年度科学技术研究项目(12511110)

摘　　要：均方概周期型函数理论在随机微分方程中的应用越来越引起数学工作者的关注,其中随机微分方程的均方渐近概周期解比均方概周期解的应用范围更加广泛。利用Banach不动点定理、线性算子解析半群理论及均方渐近概周期随机过程的概念和基本性质,研究了实可分的Hilbert空间上的一类随机微分方程的均方渐近概周期温和解的存在性和唯一性。The application of the theory of square-mean almost periodic type functions to stochastic differential equations has attracted more and more attention by researchers.The square-mean asymptotically almost periodic solutions of stochastic differential equations have a wider range of applications than square-mean almost periodic solutions.In this paper,the existence and uniqueness of the square-mean asymptotically almost periodic mild solutions of a class of stochastic differential equations in real separable Hilbert spaces are discussed,using the Banach fixed point theorem,analytic semigroup theory of linear operators and the concept and basic properties of the square-mean asymptotically almost periodic stochastic processes.

关 键 词：均方渐近概周期温和解 随机微分方程 BANACH不动点定理 线性算子解析半群 

分 类 号：O175[理学—数学]