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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

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Official URL: http://dx.doi.org/10.1016/j.anihpc.2017.09.002

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of 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:
DateEvent
July 2018Published
22 September 2017Available
11 September 2017Accepted
Volume: 35
Number: 4
Page Range: pp. 945-969
DOI: 10.1016/j.anihpc.2017.09.002
Status: Peer Reviewed
Publication Status: Published
Publisher Statement: © 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

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