@article{9e46c7304f2b492a865bacef9676c2f9,
title = "Quadratic transportation inequalities for sdes with measurable drift",
abstract = "Let X be the solution of a stochastic differential equation in Euclidean space driven by standard Brownian motion, with measurable drift and Sobolev diffusion coefficient. In our main result we show that when the drift is measurable and the diffusion coefficient belongs to an appropriate Sobolev space, the law of X satisfies Talagrand's inequality with respect to the uniform distance.",
keywords = "Quadratic transportation inequality, Singular drifts, Sobolev regularity, Stochastic differential equations",
author = "KHALED BAHLALI and SOUFIANE MOUCHTABIH and LUDOVIC TANGPI",
note = "Funding Information: Received by the editors March 26, 2020, and, in revised form, August 3, 2020, August 18, 2020, September 22, 2020, and October 24, 2020. 2020 Mathematics Subject Classification. Primary 60E15, 60H20, 60J60, 28C20. Key words and phrases. Quadratic transportation inequality, stochastic differential equations, singular drifts, Sobolev regularity. The second author was supported by PHC Toubkal 18/59. The third author was supported by NSF grant DMS-2005832. Publisher Copyright: {\textcopyright} 2021 American Mathematical Society. All rights reserved.",
year = "2021",
doi = "https://doi.org/10.1090/proc/15477",
language = "American English",
volume = "149",
pages = "3583--3596",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "8",
}