Abstract
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 (Unterberger, Commun Math Phy 298(1):1–36, 2010) 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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Unterberger, J. A Renormalized Rough Path over Fractional Brownian Motion. Commun. Math. Phys. 320, 603–636 (2013). https://doi.org/10.1007/s00220-013-1707-0
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DOI: https://doi.org/10.1007/s00220-013-1707-0