Yamada-Watanabe定理是判断随机微分方程强解存在性的重要方法，Engelbert定理是Yamada-Watanbe 定理的美妙完善，可以用来证明随机微分方程解的强唯一性. 因此研究随机微分方程的Engelbert 定理对于研究随机微分方程解及其唯一性问题具有一定的科学意义. 本项目研究由一般Levy过程驱动的随机微分方程和随机发展方程的Engelbert定理, 期望在漂移项、扩算项系数仅仅满足一般可测性的条件下，得到在实际应用中更容易判断的简化形式的Engelbert定理，然后应用该定理研究随机发展方程的解的存在唯一性. 本项目以带跳形式的随机微分方程的基本理论为基础，以Poisson随机测度鞅刻画问题的研究为主线，以驱动过程与方程弱解之间的关系的研究为桥梁，以Kurtz的Yamda-Watanabe-Engelbert 结果为依据，最后得到期望的结果.

Yamada-Watanabe theorem is an important method to prove the existence of strong solutions for stochastic differential equations. Engelbert theorem is a beautiful complement for Y-W theorem, which can be used to prove the strong uniqueness for SDEs. So the study on Engelbert theorem is important in science. In this project, we mainly study the Engelbert theorem for the SDEs and stochastic evolution equations driven by general Levy processes. The aim is to get a simplified Engelbert theorem and then to study the existence and uniqueness for stochastic evolution equation by using this theorem. Firstly, we are based on the fundamental theory of SDEs with jumps. Secondly, we study the martingale characteristic for Poisson process and general Levy process. After that, we construct the the relationship between the driven terms and the weak solutions of the SDEs. Finally, the theorem will be proved by using Kurtz’s result.