Riedel, Sebastian and Xu, Weijun (2013) A simple proof of distance bounds for Gaussian rough paths. Electronic Journal of Probability, Volume 18 . pp. 1-18. doi:10.1214/EJP.v18-2387

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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.

Item Type:	Journal Article
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Electronic Journal of Probability
Publisher:	University of Washington. Dept. of Mathematics
ISSN:	1083-6489
Official Date:	30 December 2013
Dates:	Date Event 30 December 2013 Available
Volume:	Volume 18
Page Range:	pp. 1-18
DOI:	10.1214/EJP.v18-2387
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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