2004/12/09 by Annie Millet, A MILLET, Marta Sanz–Solé +1 · 51 citations
Economics, Econometrics and Finance · Mathematics · #Brownian motion #Financial Risk and Volatility Modeling #Fractional Brownian motion #Gaussian #Geometry #Hurst exponent #Mathematical analysis #Mathematics #Physics #Product (mathematics) #Pure mathematics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60F10 #msc:60G15
paper · pdf · open access · doi:10.1016/j.anihpb.2005.04.003
published in Annales de l Institut Henri Poincaré Probabilités et Statistiques 42(2), 245-271 (Institute of Mathematical Statistics) · 32 pages
arxiv created 2004/12/09 · openalex publication_date 2005/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Starting from the construction of a geometric rough path associated with a fractional Brownian motion with Hurst parameter H∈]1/4, 1/2[ given by Coutin and Qian (2002), we prove a large deviation principle in the space of geometric rough paths, extending classical results on Gaussian processes. As a by-product, geometric rough paths associated to elements of the reproducing kernel Hilbert space of the fractional Brownian motion are obtained and an explicit integral representation is given.