A renormalized rough path over fractional Brownian motion

2010/06/29 by Jérémie Unterberger, Unterberger, Jeremie
Economics, Econometrics and Finance · Mathematics · #05C05 #16W30 #60F05 #60G15 #60G18 #60H05 #Advanced Topics in Algebra #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1006.5604

openalex publication_date 2010/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeUnt-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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• From constructive field theory to fractional stochastic calculus. (I) The Lévy area of fractional Brownian motion with Hurst index α∈ (1/8,1/4)

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