Decay rate of iterated integrals of branched rough path

Boedihardjo, H. (2018) Decay rate of iterated integrals of branched rough path. Annales de l'Institut Henri Poincare (C) Analyse Non Linéaire, 35 (4). pp. 945-969. ISSN 0294-1449 doi: 10.1016/j.anihpc.2017.09.002

Abstract/Summary

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	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/67377
Identification Number/DOI	10.1016/j.anihpc.2017.09.002
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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