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Approximation of rough paths of fractional Brownian motion

Abstract

We consider a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]\frac{1}{4}, \frac{1}{2}[$. We give an approximation result in a modulus type distance, up to the second order, by means of a sequence of rough paths lying above elements of the reproducing kernel Hilbert space.
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Dates and versions

hal-00008790 , version 1 (15-09-2005)
hal-00008790 , version 2 (15-09-2005)

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Cite

Annie Millet, Marta Sanz-Solé. Approximation of rough paths of fractional Brownian motion. Birkhauser. Seminar on Stochastic Analysis, Random Fields and Applications V, 59 (1), Birkhauser, pp.275-304, 2008, Progresses in Probability, 59, ⟨10.1007/978-3-7643-8458-6_16⟩. ⟨hal-00008790v2⟩
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