A Dual Yamada-Watanabe Theorem for Levy driven stochastic differential equations
Probability
2021-03-29 v2
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.
Cite
@article{arxiv.2010.11579,
title = {A Dual Yamada-Watanabe Theorem for Levy driven stochastic differential equations},
author = {David Criens},
journal= {arXiv preprint arXiv:2010.11579},
year = {2021}
}
Comments
Revised version to appear in Electronic Communications in Probability