Universität zu Köln

Riedel, Sebastian (2017). Transportation-cost inequalities for diffusions driven by Gaussian processes. Electron. J. Probab., 22. SEATTLE: UNIV WASHINGTON, DEPT MATHEMATICS. ISSN 1083-6489

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Abstract

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 Frechet 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Riedel, Sebastian UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-247249
DOI:	10.1214/17-EJP40
Journal or Publication Title:	Electron. J. Probab.
Volume:	22
Date:	2017
Publisher:	UNIV WASHINGTON, DEPT MATHEMATICS
Place of Publication:	SEATTLE
ISSN:	1083-6489
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ROUGH DIFFERENTIAL-EQUATIONS; INTEGRABILITY; PATHS Multiple languages Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/24724