Quadratic transportation inequalities for sdes with measurable drift

KHALED BAHLALI, SOUFIANE MOUCHTABIH, LUDOVIC TANGPI

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)3583-3596
Number of pages14
JournalProceedings of the American Mathematical Society
Volume149
Issue number8
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Quadratic transportation inequality
  • Singular drifts
  • Sobolev regularity
  • Stochastic differential equations

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