Electronic Journal of Probability

Transportation–cost inequalities for diffusions driven by Gaussian processes

Sebastian Riedel

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We prove transportation–cost inequalities for the law of SDE solutions driven by general Gaussian processes. Examples include the fractional Brownian motion, but also more general processes like bifractional Brownian motion. In case of multiplicative noise, our main tool is Lyons’ rough paths theory. We also give a new proof of Talagrand’s transportation–cost inequality on Gaussian Fréchet spaces. We finally show that establishing transportation–cost inequalities implies that there is an easy criterion for proving Gaussian tail estimates for functions defined on that space. This result can be seen as a further generalization of the “generalized Fernique theorem” on Gaussian spaces [FH14, Theorem 11.7] used in rough paths theory.

Article information

Electron. J. Probab., Volume 22 (2017), paper no. 24, 26 pp.

Received: 21 September 2016
Accepted: 21 February 2017
First available in Project Euclid: 4 March 2017

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Zentralblatt MATH identifier

Primary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 60F10: Large deviations 60G15: Gaussian processes 60H10: Stochastic ordinary differential equations [See also 34F05]

bifractional Brownian motion concentration of measure Gaussian processes rough paths stochastic differential equations transportation inequalities

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Riedel, Sebastian. Transportation–cost inequalities for diffusions driven by Gaussian processes. Electron. J. Probab. 22 (2017), paper no. 24, 26 pp. doi:10.1214/17-EJP40. https://projecteuclid.org/euclid.ejp/1488596710

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