Large deviations for rough paths of the fractional Brownian motion

By Annie Millet, Marta Sanz-Sol'e. 2004

48 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8ab7c2f23f12b81a8711154a9ce07f54191e378b

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Citations in the corpus

Integrability of (Non-)Linear Rough Differential Equations and Integrals (2011, methodology): “of rather deep facts from (Gaussian) rough paths theory - notably Lyons’ extension theorem [21] in the quantitative form due to the neo-classical inequality, large deviations for Gaussian rough paths [24, 12] and a recent Cameron–Martin / ρ-variation embedding theorem [13, 14] - the generalization i”
Rough path analysis via fractional calculus (2006, background): “A large deviation principle has been obtained in [14] for these equations.”
Differential equations driven by Gaussian signals (2007, background): “The embedding (2) is absolutely crucial for these purposes: given ρ 2 it tells us that elements in H (and in particular, Karhunen-Loeve approximations which are finite sums of form (3)) admit canoncially defined second and third iterated integrals.”