A REVIEW OF THE Pth MOMENT EXPONENTIAL STABILITY AND ALMOST SURE EXPONENTIAL STABILITY OF NON-LINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH CONSTANT TIME LAG.

The paper tries to connect the pth- moment exponential stability and the almost sure exponential stability of non-linear stochastic delay differential equations (SDDEs) with small time lag. It is generally true that the pth- moment exponential stability of SDDEs and the almost sure exponential stability do not imply each other. By applying the Lyapunov function and an idea of generalized moment inequality as well as Borel- Cantelli lemma, it is established that under certain conditions on the drift and diffusion coefficients, the Pth moment exponential stability implies the almost sure exponential stability. To illustrate the effectiveness of the main result an example is presented.