Decay rate of iterated integrals of branched rough pathBoedihardjo, 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
It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.anihpc.2017.09.002 Abstract/SummaryIterated 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.
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