Hurst exponent estimation of Fractional Lévy Motion

In this paper, we build an estimator of the Hurst exponent of a fractional Lévy motion based on its wavelet coefficients. The stochastic process is observed with random noise errors in the following framework: continuous time and discrete observation times. In both cases, we prove consistency of our wavelet type estimator. Moreover we perform some simulations in order to study numerically the asymptotic behaviour of this estimate