Theoretical and numerical comparisons of the parameter estimator of the fractional Brownian motion

International audienceThe fractional Brownian motion which has been defined by Kolmogorov \cite{k40} and numerous papers was devoted to its study since its study in Mandelbrot and Van Ness \cite{MvN:68} present it as a paradigm of self-similar processes. The self-similarity parameter, also called the Hurst parameter, commands the dynamic of this process and the accuracy of its estimation is often crucial. We present here the main and used methods of estimation, with the limit theorems satisfied by the estimators. A numerical comparison is also provided allowing to distinguish between the estimators