A Dual Yamada-Watanabe Theorem for Levy driven stochastic differential equations

David Criens

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arXiv · 2010.11579

A Dual Yamada-Watanabe Theorem for Levy driven stochastic differential equations

David Criens

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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) Levy 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.

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David Criens. 2020-10-22. A Dual Yamada-Watanabe Theorem for Levy driven stochastic differential equations. https://arxiv.org/abs/2010.11579

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