Path-by-path uniqueness for stochastic differential equations under Krylov-R\"ockner condition
Probability
2025-07-09 v2 Classical Analysis and ODEs
Abstract
We show that any stochastic differential equation (SDE) driven by Brownian motion with drift satisfying the Krylov-R\"ockner condition has exactly one solution in an ordinary sense for almost every trajectory of the Brownian motion. Consequentially, such SDE is strongly complete and forms a random dynamical system. Also, a further application to a boundary value problem is discussed.
Cite
@article{arxiv.2304.06802,
title = {Path-by-path uniqueness for stochastic differential equations under Krylov-R\"ockner condition},
author = {Lukas Anzeletti and Khoa Lê and Chengcheng Ling},
journal= {arXiv preprint arXiv:2304.06802},
year = {2025}
}
Comments
applications of path-by-path uniqueness added in v2