# Almost Sure Exponential Stability of Stochastic Differential Delay Equations

Xuerong Mao (毛学荣)，英国Strathclyde大学数学与统计系教授，苏格兰皇家学会院士，教育部海外名师，教育部长江讲座教授，东华大学兼职特聘教授。

It was very easy to show that the linear scalar stochastic differential equation (SDE) $dx(t) = b x(t) dB(t)$ is almost surely exponentially stable as long as $b \not= 0$. However, it was nontrivial for Mohammed and Scheutzow (1997) to show if the corresponding linear scalar stochastic differential delay equation (SDDE) $dx(t) =b x(t-\tau) dB(t)$ is almost surely exponentially stable for sufficiently small $\tau$. There has been a very little progress in this topic since 1997. This talk will report some recent developments.