Factorial Decay of Iterated Rough Integrals

TL;DR

This paper offers an alternative proof for the factorial decay estimate of iterated integrals in geometric rough paths, simplifying the proof process and extending Lyons' foundational work to broader contexts.

Contribution

It provides a new proof method avoiding the neoclassical inequality, applicable to branched rough paths, enhancing understanding of rough path theory.

Findings

Proof of factorial decay estimate without neoclassical inequality

Extension of Lyons' 94' results to geometric rough paths

Applicable to branched rough paths

Abstract

In this complementary note to [1] (arXiv:1501.05641), we provide an alternative proof for the factorial decay estimate of iterated integrals for geometric rough paths without using the neoclassical inequality. This note intends to aid the readers on the proof in [1] which works also for branched rough paths. Just as in [1], the proof here is an extension of Lyons 94' [4] from Young's integration to geometric rough paths.