Quadratic transportation inequalities for SDEs with measurable drift

Bahlali, Khaled; Mouchtabih, Soufiane; Tangpi, Ludovic

doi:10.1090/proc/15477

Quadratic transportation inequalities for SDEs with measurable drift
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by Khaled Bahlali, Soufiane Mouchtabih and Ludovic Tangpi

Proc. Amer. Math. Soc. 149 (2021), 3583-3596

DOI: https://doi.org/10.1090/proc/15477

Published electronically: May 18, 2021

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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.

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