It is proposed a text-independent automatic speaker recognition (ASkR) system which employs a new speech feature and a new classifier. The statistical feature pH is a vector of Hurst parameters obtained by applying a wavelet-based multi-dimensional estimator (M dim wavelets) to the windowed short-time segments of speech. The proposed classifier for the speaker identification and verification tasks is based on the multi-dimensional fBm (fractional Brownian motion) model, denoted by M dim fBm. For a given sequence of input speech features, the speaker model is obtained from the sequence of vectors of H parameters, means and variances of these features.