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• W3103605883 abstract "We construct in this article an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/alpha$-variation for any $alphain(0,1)$. The method may be coined as 'Fourier normal ordering', since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies. In doing so, there appear non-trivial tree combinatorics, which are best understood by using the structure of the Hopf algebra of decorated rooted trees (in connection with the Chen or multiplicative property) and of the Hopf shuffle algebra (in connection with the shuffle or geometric property). Holder continuity is proved by using Besov norms. The method is well-suited in particular in view of applications to probability theory (see the companion article cite{Unt09} for the construction of a rough path over multidimensional fractional Brownian motion with Hurst index $alpha<1/4$, or cite{Unt09ter} for a short survey in that case)." @default.
• W3103605883 created "2020-11-23" @default.
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• W3103605883 date "2010-05-19" @default.
• W3103605883 modified "2023-10-16" @default.
• W3103605883 title "Hölder-Continuous Rough Paths by Fourier Normal Ordering" @default.
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• W3103605883 doi "https://doi.org/10.1007/s00220-010-1064-1" @default.
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