Parameter estimation of a fractional Brownian motion in a white noise using wavelets

To discriminate the fractal parameter of a fractional Brownian motion (fBm) embedded in a white noise is equivalent to discriminating the composite singularity formed by superimposing a peak singularity upon a Dirac singularity. We use the autocorrelation of the wavelet transform coefficients to characterize the composite singularity, by formalizing this problem as a nonlinear optimization problem. We modify the internal penalty function method to efficiently estimate the parameters of the fBm in the white noise