Stability Of The CSST Approximation Of Stochastic Delay Differential Equations With Possion Jumps

Stochastic delay differential equations(SDDEs) are widely used in engineering, )hysics, medical science, biology, economics and so on. Since most of these equations ;annot be solved explicitly, numerical approximations become an important tool in studying the properties of these stochastic systems. In this thesis, we mainly study the stability of the numerical methods for SDDEs with poisson jumps and the almost sure sxponential stability of the compensated split-step theta (CSST) method of stochastic delay differential equations with poisson jumps..In the third chapter, we discussed the compensation method (CSST) for ? ?g [0,0.5],the properties of the almost sure exponential stability. The results show that for ?? [0,0.5], with the linear growth condition, the CSST method can keep the almost sure sxponential stability of the analytical solution. In the three chapter,discussed the CSST n? ?(0.5,1], even without the linear growth condition, the CSST method can also inherit from the analytical solution properties of the almost sure exponential stability. In the four chapter, We used coupled monotone condition. For?? [0,0.5] under the linear growth condition, the CSST method has the same properties in the three chapter. The discussion in the four chapter, for?? (0.5,1] even without the linear growth condition, the CSST method has the same properties of corresponding in three chapter.