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arXiv · 1501.05641

Decay Rate of Iterated Integrals of Branched Rough Paths

Horatio Boedihardjo
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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.

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Horatio Boedihardjo. 2015-01-22. Decay Rate of Iterated Integrals of Branched Rough Paths. https://doi.org/10.1016/j.anihpc.2017.09.002

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