Strong Solutions of a Class of Stochastic Differential Equations with Jumps

Abstract

We study a class of stochastic integral equations with jumps under non-Lipschitz conditions. We use the method of Euler approximations to obtain the existence of the solution and give some sufficient conditions for the strong uniqueness.

Keywords:

• Euler approximation
• Existence
• Jump
• Non-Lipschitz
• Stochastic equations
• Strong solution
• Uniqueness

Mathematics Subject Classification:

• Primary 60H20
• Secondary 60H10

I thank the referees for helpful comments that improve both the presentation and contents of this article. This article is based on a graduation thesis at Beijing Normal University. I would like to give my sincere thanks to my supervisor Professor Zenghu Li for his encouragement and helpful suggestions. This research was supported by National Science Foundation of China (No. 10721091).