A multifractal analysis based on evaluation and interpretation of Large Deviation spectra is applied to plasma edge turbulence data from different devices (MAST and Tore Supra). It is demonstrated that in spite of some universal features there are unique characteristics for each device as well as for different confinement regimes. In the second part of the exposition the issue of estimating the variable power law behavior of spectral densities is addressed. The analysis of this issue is performed using fractional Brownian motion (fBm) as the underlying stochastic model whose parameters are estimated locally in time by wavelet scale spectra. In such a manner information about the inertial range as well as variability of the fBm parameters is obtained giving more information important for understanding edge turbulence and intermittency
