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We prove a dual Yamada-Watanabe theorem for one-dimensional stochasticdifferential equations driven by quasi-left continuous semimartingales withindependent increments. In particular, our result covers stochasticdifferential equations driven by (time-inhomogeneous) Levy processes. Moreprecisely, we prove that weak uniqueness, i.e. uniqueness in law, implies weakjoint uniqueness, i.e. joint uniqueness in law for the solution process and itsdriver.

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