| Differential equation is an important tool to describe the objective change of matters. Because of the existence of random disturbance, the famous Japanese mathematician?Ito added a disturbance factor to the equation. That is how the?Ito stochastic differential equation come into being.The random system mentioned above takes the white gaussian noise as the only disturbance. However, in everyday life, the system is often interrupted by many other factors. To solve this problem, Wu Han and Ming first advocated selective stochastic differential equations motivated by general stochastic sequence.The paper is aimed to make a qualitative research about the equation. We mainly study the existence,uniqueness, p-moment uniform boundedness and the almost surely exponential stability of stochastic differential equations with jumps in this thesis.In Chapter 3,we study the existence and uniqueness of stochastic differential equations with jumps by Pearson iteration method. The article makes use of iterative method to achieve the desired results includes some inequalities,Lipschtiz conditions.The the existence and uniqueness of the solution of equation will be the important reference and basis for any other theories.This chapter is the basis of other theorise.In Chapter 4,we do research on the p-moment uniform boundedness of stochastic differential equations with jumps.Based on the theory of?Ito ’s stochastic calculus,by means of Liapunov’s indirect method some sufficient conditions for p-moment uniform boundedness of the system are presented.Enriched the existing literature results.The method can be used to apply in other fields research of stochastic differential equations with jumps.In Chapter 5,we do research on the almost surely exponential stability of stochastic differential equations with jumps.By employing the method of vector Lyapunov functions, Lemma Borel-Cantelli and some techniques in stochastic analysis some sufficient conditions for the almost surely exponential stability areestablished.The obtained results improve the corresponding known results. |
