This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several differen...This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.展开更多
The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equa...The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.展开更多
This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment ...This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.展开更多
This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations wi...This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations with delay. A new kind of φ-function is introduced to address the stability, which is more general than the exponential stability and polynomial stability. Using a specific Lyapunov function, a stability criteria for the neutral stochastic differential equations with multiple variable delays is established, by which it is relatively easy to verify the stability of such equations. Finally, the proposed theories are illustrated by two examples.展开更多
基金Supported by NSFC (11001091)Chinese UniversityResearch Foundation (2010MS129)
文摘This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.
基金Sponsored by HUST Foundation(0125011017)the National NSFC under grant(70671047)
文摘The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.
文摘This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.
基金The National Natural Science Foundation of China (No.10671078)
文摘This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations with delay. A new kind of φ-function is introduced to address the stability, which is more general than the exponential stability and polynomial stability. Using a specific Lyapunov function, a stability criteria for the neutral stochastic differential equations with multiple variable delays is established, by which it is relatively easy to verify the stability of such equations. Finally, the proposed theories are illustrated by two examples.
