A renormalized rough path over fractional Brownian motion

Details A renormalized rough path over fractional Brownian motion A renormalized rough path over fractional Brownian motion

2010-06-29

arxiv.org/abs/1006.5604v1

Mathematics

Probability

46 pages, 6 figures

Scientific paper

We construct in this article a rough path over fractional Brownian motion with arbitrary Hurst index by (i) using the Fourier normal ordering algorithm introduced in \cite{Unt-Holder} to reduce the problem to that of regularizing tree iterated integrals and (ii) applying the Bogolioubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization algorithm to Feynman diagrams representing tree iterated integrals.

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