随机泛函微分方程的渐近稳定性

应用多个Liapunov函数讨论了随机泛函微分方程解的渐近行为，建立了确定这种方程解的极限位置的充分条件，并且从这些条件得到了随机泛函微分方程渐近稳定性的有效判据，使实际应用中构造Liapunov函数更为方便．同时也说明了该结果包含了经典的随机泛函微分方程稳定性结果为其特殊情况．最后给出的结果在随机Hopfield神经网络中的应用．

Asymptotic Stabilities of Stochastic Functional Differential Equations

Asymptotic characteristic of the solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Liapunov functions for locating the limit set of the solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Liapunov functions much more easily in application were obtained. The results show that the well-known classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify the results.