Open Access
2017 Transportation–cost inequalities for diffusions driven by Gaussian processes
Sebastian Riedel
Electron. J. Probab. 22: 1-26 (2017). DOI: 10.1214/17-EJP40


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.


Download Citation

Sebastian Riedel. "Transportation–cost inequalities for diffusions driven by Gaussian processes." Electron. J. Probab. 22 1 - 26, 2017.


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

zbMATH: 1373.60072
MathSciNet: MR3622894
Digital Object Identifier: 10.1214/17-EJP40

Primary: 28C20 , 60F10 , 60G15 , 60H10

Keywords: bifractional Brownian motion , concentration of measure , Gaussian processes , Rough paths , Stochastic differential equations , Transportation inequalities

Vol.22 • 2017
Back to Top