2016
DOI: 10.4236/am.2016.78070
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Equivalence of Uniqueness in Law and Joint Uniqueness in Law for SDEs Driven by Poisson Processes

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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Cited by 3 publications
(10 citation statements)
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“…A version for SDEs with Lévy drivers seems to be missing in the literature. To the best of our knowledge, the only formulation of a dual theorem for SDEs with discontinuous noise is the main result of [23], which is a version for SDEs driven by time-inhomogeneous Poisson processes. However, the proof in [23] has a gap.…”
Section: Introductionmentioning
confidence: 99%
See 4 more Smart Citations
“…A version for SDEs with Lévy drivers seems to be missing in the literature. To the best of our knowledge, the only formulation of a dual theorem for SDEs with discontinuous noise is the main result of [23], which is a version for SDEs driven by time-inhomogeneous Poisson processes. However, the proof in [23] has a gap.…”
Section: Introductionmentioning
confidence: 99%
“…To the best of our knowledge, the only formulation of a dual theorem for SDEs with discontinuous noise is the main result of [23], which is a version for SDEs driven by time-inhomogeneous Poisson processes. However, the proof in [23] has a gap. 1 The purpose of this short paper is to close the gap in the literature and to prove a dual theorem for SDEs driven by quasi-left continuous semimartingales with independent increments (SIIs), which is a large class of drivers including in particular all Lévy processes.…”
Section: Introductionmentioning
confidence: 99%
See 3 more Smart Citations