Stochastic transport equation with bounded and Dini continuous drift
Probability
2021-07-29 v2
Abstract
The results established by Flandoli, Gubinelli and Priola ({\it Invent. Math.} {\bf 180} (2010) 1--53) for stochastic transport equation with bounded and H\"{o}lder continuous drift are generalized to bounded and Dini continuous drift. The uniqueness of -solutions is established by the It\^o--Tanaka trick partially solving the uniqueness problem, which is still open, for stochastic transport equation with only bounded measurable drift. Moreover the existence and uniqueness of stochastic diffeomorphisms flows for a stochastic differential equation with bounded and Dini continuous drift is obtained.
Cite
@article{arxiv.2105.08465,
title = {Stochastic transport equation with bounded and Dini continuous drift},
author = {Jinlong Wei and Guangying Lv and Wei Wang},
journal= {arXiv preprint arXiv:2105.08465},
year = {2021}
}
Comments
39pages