Decay Rate of Iterated Integrals of Branched Rough Paths
Probability
2017-10-02 v4 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.1501.05641,
title = {Decay Rate of Iterated Integrals of Branched Rough Paths},
author = {Horatio Boedihardjo},
journal= {arXiv preprint arXiv:1501.05641},
year = {2017}
}
Comments
26 pages, 2 figures. Accepted version