Large deviations for rough paths of the fractional brownian motion
Annie Millet, Marta Sanz-Solé (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Large deviations for rough paths of the fractional brownian motion
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In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order ≥2 of the fractional brownian motion with Hurst parameter ∈(0, 1), where is an integer. The central limit holds for 1/2<≤1−1/2, the limit being a conditionally gaussian distribution. If <1/2 we show the convergence in 2 to a limit which only depends on the fractional brownian motion, and if >1−1/2 we show the convergence in 2 to a stochastic integral...