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.
Highlights
Engelbert got an inverse result, that is Strong solution + Joint uniqueness in law ⇒ Pathwise uniqueness, which can be seen as a complement of the Yamada-Watanabe theorem
In this paper, we are concerned with the following onedimensional stochastic differential equation driven by Poisson process
We will give an extension form of Watanabe’s characterization for 2-dimensional Poisson process, by applying Cherny’s approach, we prove the equivalence of the uniqueness in law and joint uniqueness in law for Equation (1)
Summary
Uniqueness in Law, Joint Uniqueness in Law, Poisson Process, Engelbert Theorem (2016) Equivalence of Uniqueness in Law and Joint Uniqueness in Law for SDEs Driven by Poisson Processes. Engelbert got an inverse result, that is Strong solution + Joint uniqueness in law ⇒ Pathwise uniqueness, which can be seen as a complement of the Yamada-Watanabe theorem. In this paper, we are concerned with the following onedimensional stochastic differential equation driven by Poisson process
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