Quadratic transportation inequalities for sdes with measurable drift

KHALED BAHLALI; SOUFIANE MOUCHTABIH; LUDOVIC TANGPI

doi:10.1090/proc/15477

Quadratic transportation inequalities for sdes with measurable drift

KHALED BAHLALI, SOUFIANE MOUCHTABIH, LUDOVIC TANGPI

Operations Research & Financial Engineering

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Pages (from-to)	3583-3596
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	149
Issue number	8
DOIs	https://doi.org/10.1090/proc/15477
State	Published - 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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10.1090/proc/15477

Cite this

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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 = "10.1090/proc/15477",

language = "English (US)",

volume = "149",

pages = "3583--3596",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

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TY - JOUR

T1 - Quadratic transportation inequalities for sdes with measurable drift

AU - BAHLALI, KHALED

AU - MOUCHTABIH, SOUFIANE

AU - TANGPI, LUDOVIC

N1 - 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: © 2021 American Mathematical Society. All rights reserved.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Quadratic transportation inequality

KW - Singular drifts

KW - Sobolev regularity

KW - Stochastic differential equations

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -

Quadratic transportation inequalities for sdes with measurable drift

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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