Abstract
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 in [Probab. Theory Related Fields 122 (2002) 108–140], 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.
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