科研之友
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摘要
It is well known that for two p-rough paths, if their first left perpindicularpright perpindicular levels of iterated integrals are close in p-variation sense, then all levels of their iterated integrals are close. In this paper, we prove that a similar result holds for the paths provided the first left perpindicularpright perpindicular terms are close in a 'uniform' sense. The estimate is explicit, dimension free, and only involves the p-variation of two paths and the 'uniform' distance between the first left perpindicularpright perpindicular terms. Applications include estimation of the difference of the signatures of two uniformly close paths (Lyons and Xu, 2011 [6]), and convergence rates for Gaussian rough paths (Riedel and Xu, 2012 [7]). () 2013 Elsevier Masson SAS.
- 出版日期2013-11
