Nonparametric estimation of the local Hurst function of multifractional processes

Consistency, almost sure convergence and central limit theorems are provided for two nonparametric estimators of the local Hurst function of Gaussian multifractional processes. In the case of multifractional Brownian motions, we correct results of Coeurjolly (2005) \cite{coeur2005} and Benassi {\it et al.} (1998a) \cite{ben1998a}.