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We prove transportation-cost inequalities for the law of SDE solutions driven by general Gaussian processes.
An inequality of the Hölder type, connected with Stieltjes integration
Laurence C. Young · 1936
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Fractional Brownian motions, fractional noises and applications
Benoit B. Mandelbrot and John W. Van Ness · 1968
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Extremal properties of half-spaces for spherically invariant measures
V. N. Sudakov and B. S. Cirel ′ · 1974
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The Brunn-Minkowski inequality in Gauss space
Christer Borell · 1975
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A simple proof of the blowing-up lemma
Katalin Marton · 1986
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Some deviation inequalities
B. Maurey · 1991
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The structure of measurable mappings on metric spaces
Andrzej Wiśniewski · 1994
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Isoperimetry and Gaussian analysis
Michel Ledoux · 1996
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Bounding d ¯ \overline{d} -distance by informational divergence: a method to prove measure concentration
Katalin Marton · 1996
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Transportation cost for Gaussian and other product measures
Michel P. Talagrand · 1996
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Gaussian measures
Vladimir I. Bogachev · 1998
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Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
Sergey G. Bobkov and Friedrich Götze · 1999
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
Felix Otto and Cédric Villani · 2000
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Inégalités de Sobolev logarithmiques et hypercontractivité en mécanique statistique et en EDP
Ivan Gentil · 2001
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The concentration of measure phenomenon
Michel Ledoux · 2001
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Stochastic analysis, rough path analysis and fractional Brownian motions
Laure Coutin and Zhongmin Qian · 2002
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System control and rough paths
Terry J. Lyons and Zhongmin Qian · 2002
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An example of infinite dimensional quasi-helix
Christian Houdré and José Villa · 2003
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Topics in optimal transportation
Cédric Villani · 2003
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Transportation cost-information inequalities and applications to random dynamical systems and diffusions
Hacene Djellout, Arnaud Guillin, and Li-ming Wu · 2004
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Monge-Kantorovitch measure transportation and Monge-Ampère equation on Wiener space
Denis Feyel and Ali S. Üstünel · 2004
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Differential equations driven by rough paths
Terry J. Lyons, Michael Caruana, and Thierry Lévy · 2004
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Talagrand’s T 2 T_{2} -transportation inequality w.r.t. a uniform metric for diffusions
Li-ming Wu and Zheng-liang Zhang · 2004
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Transportation inequalities for SDEs involving fractional Brownian motion and standard Brownian motion
Toufik Guendouzi · 2012
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Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion
Bruno Saussereau · 2012
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Transportation cost inequalities for diffusions under uniform distance
Ali Suleyman Üstünel · 2012
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Sonja Cox, Martin Hutzenthaler, and Arnulf Jentzen · 2013
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Integrability and tail estimates for Gaussian rough differential equations
Thomas Cass, Christian Litterer, and Terry J. Lyons · 2013
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On bifractional Brownian motion
Francesco Russo and Ciprian A. Tudor · 2006
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A large deviation approach to some transportation cost inequalities
Nathael Gozlan and Christian Léonard · 2007
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Wiener integrals, Malliavin calculus and covariance measure structure
Ida Kruk, Francesco Russo, and Ciprian A. Tudor · 2007
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A concise course on stochastic partial differential equations
Claudia Prévôt and Michael Röckner · 2007
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A characterization of dimension free concentration in terms of transportation inequalities
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An Introduction to Stochastic PDEs
Martin Hairer · 2009
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Integrability of (non-)linear rough differential equations and integrals
Peter K. Friz and Sebastian Riedel · 2013
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From log Sobolev to Talagrand: a quick proof
Nicola Gigli and Michel Ledoux · 2013
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Solving the KPZ equation
Martin Hairer · 2013
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A Course on Rough Paths with an introduction to regularity structures
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A theory of regularity structures
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A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations
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Paracontrolled distributions and singular PDEs
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From rough path estimates to multilevel Monte Carlo
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The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
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Strong completeness and semi-flows for stochastic differential equations with monotone drift
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