Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

A simple proof of distance bounds for Gaussian rough paths

Tools
- Tools
+ Tools

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

[img]
Preview
PDF
WRAP_2387-15785-1-PB.pdf - Published Version - Requires a PDF viewer.
Available under License Creative Commons Attribution.

Download (437Kb) | Preview
Official URL: http://dx.doi.org/10.1214/EJP.v18-2387

Request Changes to record.

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:
DateEvent
30 December 2013Available
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

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us