Decay Rate of Iterated Integrals of Branched Rough Paths
arXiv:1501.05641 · doi: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.
26 pages, 2 figures. Accepted version
Cited by in corpus (7)
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- Planarly branched rough paths and rough differential equations on homogeneous spaces
- An isomorphism between branched and geometric rough paths
- A remainder estimate for branched rough differential equations
- Branched Itô formula and natural Itô-Stratonovich isomorphism
- Factorial Decay of Iterated Rough Integrals
- Rough path theory