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Equivalence of Uniqueness in Law and Joint Uniqueness in Law for SDEs Driven by Poisson Processes

DOI: 10.4236/am.2016.78070, PP. 784-792

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

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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.

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