A uniform estimate for rough paths

Details A uniform estimate for rough paths A uniform estimate for rough paths

2011-10-24

arxiv.org/abs/1110.5278v4

Mathematics

Probability

12 pages

Scientific paper

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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