一类随机微分方程的均方渐近概自守温和解  

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

作　　者：姚慧丽[1] 刘婷[1] 张士晶[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2016年第3期114-120,共7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：随机微分方程是为解决自然科学现象建立起来的一类数学模型,其均方渐近概自守温和解比均方概自守温和解具有更广的应用范围.介绍了均方渐近概自守随机过程的概念和一些基本性质,利用Banach不动点定理、卷积族的指数稳定性及均方渐近概自守随机过程的相关性质,研究了实可分的Hilbert空间中一类具有延迟的非自治随机微分方程的均方渐近概自守温和解的存在性和唯一性.Stochastic differential equations are the problem of phenomena in the natural science. a class of mathematical models, which are established to solve Square-mean asymptotically almost automorphic mild solutions of stochastic differential equations have a wider application range than square-mean almost automorphic mild solutions. The definition of square-mean asymptotically almost automorphic stochastic processes and some basic properties are introduced. The existence and uniqueness of square-mean asymptotically almost automorphic solutions of non-auton- omous stochastic differential equations with delay in a real separable Hilbert space are studied, by using the Banach fixed point theorem, the exponential stability of convolution family and the related properties of the square-mean as- ymptotically almost automorphic stochastic processes.

关 键 词：均方渐近概自守温和解 随机微分方程 BANACH不动点定理 卷积族 

分 类 号：O175[理学—数学]