The Analysis Of Stability For The Stochastic Differential Equations With Poisson Jumps

This paper discusses the pth moment exponential stability and almost sure exponential stability of stochastic differential equations with Poisson jumps . We don't use the method of common Lyapunov function and demonstrates the effectiveness of random 9 method on the pth moment exponential stability and almost sure exponential stability for stochastic differential equations with Poisson jumps .The main content of this paper consists of two parts:The first part gives a set of conditions for numerical methods, we prove that if the numerical methods satisfy these conditions, then the pth moment exponential stability of the stochastic differential equa-tions with Poisson jumps is equivalent to the pth moment exponential stability of numerical method .The second part introduces the stochastic ? method, and verify the method satisfies a set of conditions were given in last chapter.It is proved that the pth moment exponential stability of stochastic 9 method is equivalent to the pth moment exponential stability of stochastic differential equations with Poisson jumps. It means that the simulation of random ? method is effective for the pth moment exponential stability of stochastic differential equations with Poisson jumps . Then the results are extended to the almost sure exponential stability.At the end of the paper, some problems which can be further discussed in the future are given.