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Decay rate of iterated integrals of branched rough paths
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Boedihardjo, Horatio (2018) Decay rate of iterated integrals of branched rough paths. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 35 (4). pp. 945-969. doi:10.1016/j.anihpc.2017.09.002 ISSN 0294-1449.
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Official URL: http://dx.doi.org/10.1016/j.anihpc.2017.09.002
Abstract
Iterated integrals of paths arise frequently in the study of the Taylor's expansion for controlled differential equations. We will prove a factorial decay estimate, conjectured by M. Gubinelli, for the iterated integrals of non-geometric rough paths. We will explain, with a counter example, why the conventional approach of using the neoclassical inequality fails. Our proof involves a concavity estimate for sums over rooted trees and a non-trivial extension of T. Lyons' proof in 1994 for the factorial decay of iterated Young's integrals.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| Library of Congress Subject Headings (LCSH): | Multiple integrals, Differential equations, Stochastic differential equations | ||||||||
| Journal or Publication Title: | Annales de l'Institut Henri Poincaré C, Analyse non linéaire | ||||||||
| Publisher: | Elsevier | ||||||||
| ISSN: | 0294-1449 | ||||||||
| Official Date: | July 2018 | ||||||||
| Dates: |
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| Volume: | 35 | ||||||||
| Number: | 4 | ||||||||
| Page Range: | pp. 945-969 | ||||||||
| DOI: | 10.1016/j.anihpc.2017.09.002 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Reuse Statement (publisher, data, author rights): | © 2018, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/. | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 22 July 2020 | ||||||||
| Date of first compliant Open Access: | 22 July 2020 |
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