一类随机微分方程均方s渐进ω周期解的存在性
EXISTENCE OF SQUARE-MEAN s-ASYMPTOTICALLY ω-PERIODIC SOLUTIONS TO SOME STOCHASTIC DIFFERENTIAL EQUATIONS

本文研究了在可分的实Hilbert空间中一类随机微分方程均方s渐进ω周期温和解的存在性问题.利用均方s渐进ω周期随机过程理论及Banach不动点定理，获得了此类方程均方s渐进ω周期温和解的存在及唯一性结果.最后给出相关例子来验证理论结果.
This paper is concerned with the existence of square-mean s-asymptotically ω-periodic mild solutions to some stochastic differential equations in a real separable Hilbert space. By using the new theorem of square-mean s-asymptotically ω-periodicity for stochastic process and Banach fixed point theorem, we obtain the existence and uniqueness of square-mean s-asymptotically ω-periodic mild solutions to the equations. To illustrate the abstract result, a concrete example is given