作者:姚慧丽，霍贵珍，孙海彤，王晶囡
Authors:YAO Hui-li,HUO Gui-zhen,SUN Hai-tong,WANG Jing-nan摘要:\n\t摘要:均方概自守型函数理论在随机微分方程中的应用越来越引起数学研究者的关注，这类方程的均方渐近概自守解比均方概自守解的应用范围更加广泛。对一类半线性随机微分方程的均方渐近概自守温和解进行探讨。利用Banach压缩映射原理，结合均方渐近概自守随机过程的定义和性质、Cauchy-Schwarz不等式、Lipschitz条件、 Ito等距积分，讨论了该类随机微分方程的均方渐近概自守温和解的存在唯一性。\n

Abstract:Abstract:The applications of the theories of square-mean almost automorphic type functions have attracted more and more attention by mathematics researchers, square-mean asymptotically almost automorphic solutions of this class of differential equations have a wider range of applications than square-mean almost automorphic solutions.Square-mean asymptotically almost automorphic mild solutions to a class of semi-linear stochastic differential equations are investigated. The existence and uniqueness of square-mean asymptotically almost automorphic mild solutions for this kind of equation are discussed by using the principle of Banach compressed image, combining with the definition and properties of square-mean asymptotically almost automorphic stochastic processes， Cauchy-Schwarz inequality, Lipschtiz conditions and Ito integrals isometry.

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