TITLE:
Equivalence of Uniqueness in Law and Joint Uniqueness in Law for SDEs Driven by Poisson Processes
AUTHORS:
Huiyan Zhao, Chunhua Hu, Siyan Xu
KEYWORDS:
Uniqueness in Law, Joint Uniqueness in Law, Poisson Process, Engelbert Theorem
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.8,
May
20,
2016
ABSTRACT: 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.