On the wavelet transform of fractional Brownian motion

A theorem characterizing fractional Brownian motion by the covariance structure of its wavelet transform is established. The authors examine whether there are alternate Gaussian processes whose wavelet transforms have a natural covariance structure. In addition, the authors examine if there are any Gaussian processes whose wavelet transform is stationary with respect to the affine group (i.e. the statistics of the wavelet transform do not depend on translations and dilations of the process)