On the pathwise uniqueness of solutions to stochastic differential equations

We give sufficient conditions for the pathwise uniqueness of solutions to nonlinear stochastic differential equations driven by Brownian motion. The result extends the classical Lipschitz uniqueness theorem and is applicable in cases where some recent pathwise uniqueness results are inconclusive. The approach repre-sents the stochastic counterpart of Constantin's recent uniqueness result [5], where a convex combination of the Nagumo and Osgood conditions was considered in the deterministic case. (c) 2023 The Author. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).