A uniform estimate for rough paths

Terry Lyons; Weijun Xu

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arXiv · 1110.5278

A uniform estimate for rough paths

Terry Lyons·Weijun Xu

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Abstract

We prove an extension to the classical continuity theorem in rough paths. We show that two $p$-rough paths are close in all levels of iterated integrals provided the first $\lfl p \rfl$ terms are close in a uniform sense. Applications include estimation of the difference of the signatures of two uniformly close paths and convergence rates of Gaussian rough paths.

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Terry Lyons, Weijun Xu. 2013-11-05. A uniform estimate for rough paths. https://arxiv.org/abs/1110.5278

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