Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H\"older-continuous rough paths by Fourier normal ordering   We construct in this article an explicit geometric rough path over arbitrary
$d$-dimensional paths with finite $1/\alpha$-variation for any
$\alpha\in(0,1)$. 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). H\"older 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).

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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th