The Pth-moment Stability Of Stochastic Differential System With Delay

Stochastic differential system with delay is an important mathematical model,which stability is a fundamental problem. Time delay and random interference often lead to the change of stability on the system, so it is necessary to study the stability of the stochastic differential system with delay. In general, it is a good technique to study the stability of the stochastic differential system with delay by constructing the appropriate Lyapunov functional or function, but it is difficult to construct the appropriate Lyapunov functional. Therefore, other technique were put out to avoid the Lyapunov functional. In the paper, inequality method will be used to obtain some results on stability for stochastic differential system with delay.Firstly, we establish a constant variant formula of the stochastic differential system with delay. By using the Jesen inequality?Burkholder-Davids-Gundy inequality and Holder in-equality, sufficient conditions for determining the pth-moment stability of stochastic differen-tial system with delay are obtained. The main results are illustrated by two examples. Secondly,the K-stability of the stochastic differential system with delay is given. On the basic of the non-negative matrices, BDG inequality and Holder inequality, sufficient conditions for determining the K-globally pth-moment asymptotically stable and the K-globally pth-moment exponentially stable are obtained.