Before revision:  By using numerical simulations and analytical considerations we show that the estimators of the Hurst exponent of the discretized process are severely negatively biased . We compute the asymptotic properties of the DFA for a generic  long memory process and we apply the result to discretized processes.
After revision:  By using numerical simulations and analytical considerations we show that the estimators of the Hurst exponent of the discretized process are severely negatively biased in finite samples. Under regularity conditions we prove that the LW estimator applied to discretized processes is consistent and asymptotically normal. Moreover, we compute the asymptotic properties of the DFA for a generic long memory process and we apply the result to discretized processes.