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A simple proof of distance bounds for Gaussian rough paths

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1.	Title	Title of document	A simple proof of distance bounds for Gaussian rough paths
2.	Creator	Author's name, affiliation, country	Sebastian Riedel; TU Berlin; Germany
2.	Creator	Author's name, affiliation, country	Weijun Xu; University of Warwick; United Kingdom
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Gaussian rough paths, iterated integrals, signatures
3.	Subject	Subject classification	60G15; 60H05; 60H10; 60H35
4.	Description	Abstract	We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assumption of their covariance functions. Similar estimates have been obtained recently in [Friz-Riedel, AIHP, to appear]. One advantage of our argument is that we obtain the bound for the third level iterated integrals merely based on the first two levels, and this reflects the intrinsic nature of rough paths. Our estimates are sharp when both covariance functions have finite $1$-variation, which includes a large class of Gaussian processes. Two applications of our estimates are discussed. The first one gives the a.s. convergence rates for approximated solutions to rough differential equations driven by Gaussian processes. In the second example, we show how to recover the optimal time regularity for solutions of some rough SPDEs.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	Berlin Mathematical School (BMS), ERC grant agreement nr. 258237, Oxford-Man Institute
7.	Date	(YYYY-MM-DD)	2013-12-30
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/2387
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-2387
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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