Abstract
We prove a dual Yamada–Watanabe theorem for one-dimensional stochastic differential equations driven by quasi-left continuous semimartingales with independent increments. In particular, our result covers stochastic differential equations driven by (time-inhomogeneous) Lévy processes. More precisely, we prove that weak uniqueness, i.e. uniqueness in law, implies weak joint uniqueness, i.e. joint uniqueness in law for the solution process and its driver.
Funding Statement
Financial support from the DFG project No. SCHM 2160/15-1 is gratefully acknowledged.
Acknowledgments
The author thanks the anonymous referee for many helpful comments.
Citation
David Criens. "A dual Yamada–Watanabe theorem for Lévy driven stochastic differential equations." Electron. Commun. Probab. 26 1 - 10, 2021. https://doi.org/10.1214/21-ECP384
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