Author(s)

Huiyan Zhao¹, Chunhua Hu¹, Siyan Xu²

¹School of Applied Mathematics, Beijing Normal University Zhuhai, Zhuhai, China.
²School of Science, Ningbo University, Ningbo, China.

We give an extension result of Watanabe’s characterization for 2-dimensional Poisson processes. By using this result, the equivalence of uniqueness in law and joint uniqueness in law is proved for one-dimensional stochastic differential equations driven by Poisson processes. After that, we give a simplified Engelbert theorem for the stochastic differential equations of this type.

Uniqueness in Law, Joint Uniqueness in Law, Poisson Process, Engelbert Theorem

Zhao, H. , Hu, C. and Xu, S. (2016) Equivalence of Uniqueness in Law and Joint Uniqueness in Law for SDEs Driven by Poisson Processes. Applied Mathematics, 7, 784-792. doi: 10.4236/am.2016.78070.