Confidence intervals for the Hurst parameter of a fractional Brownian motion based on concentration inequalities
Résumé
In this paper, we propose, for finite sample size, exact confidence intervals of the Hurst index parametrizing a fractional Brownian by using concentration inequalities. Both cases where the scaling parameter of the fractional Brownian motion is known or unknown are considered. These intervals are obtained by observing a single discretized sample path of a fractional Brownian motion and without any assumption on the parameter~$H$.
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