  In this paper, we show how concentration inequalities for Gaussian quadratic
form can be used to propose exact confidence intervals of the Hurst index
parametrizing a fractional Brownian motion. Both cases where the scaling
parameter of the fractional Brownian motion is known or unknown are
investigated. These intervals are obtained by observing a single discretized
sample path of a fractional Brownian motion and without any assumption on the
parameter $H$.
