带泊松跳的中立型随机时滞微分方程解的指数稳定性(英文)

Exponential Stability of Neutral Stochastic Delay Differential Equations with Poisson Jumps

主要利用Laypunov泛函方法和随机分析理论,研究带泊松跳的中立型随机时滞微分方程解的存在惟一性和解的指数稳定性.所得结果覆盖了许多非线性时滞微分方程已经存在的某些理论,而且实验说明此结论比以往的结论更容易验证.

The existence and the exponential stability of unique global solution for the neutral stochastic delay differential equations with Poisson jumps （NSDDEswPJs） is concerned in this paper. By applying the Lyapunov function method and the stochastic analysis theory, a criterion on exponential stability of NSDDEswPJs is discussed. The criterion not only covers many highly non-linear NSDDEswPJs with variable time delay but also can be verified much more easily than the known criteria.