中文摘要：

考虑一类线性变时滞随机微分方程，利用不动点理论，给出了零解均方渐近稳定的条件．这些条件不要求时滞有界，也不要求方程的系数函数不变号．证明了一个带有充分必要条件的均方渐近稳定性定理，改进和推广了一些相关文献的结果．

英文摘要：

In this paper we consider a linear scalar stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved. Some well-known results are improved and generalized.