We consider stationary processes with long memory which are non-Gaussian and representedas Hermite polynomials of a Gaussian process. We focus on the corresponding waveletcoefficients and study the asymptotic behavior of the sum of their squares since this sumis often used for estimating the long–memory parameter. We show that the limit is notGaussian but can be expressed using the non-Gaussian Rosenblatt process defined as aWiener–Itô integral of order 2. This happens even if the original process is definedthrough a Hermite polynomial of order higher than 2.

Lamperti's transformation, an isometry between self-similar and stationary processes, is used to solve some problems of linear estimation of continuous-time, self-similar processes. These problems include causal whitening and innovations representations on the positive real line, as well as prediction from certain finite and semi-infinite intervals. The method is applied to the specific case of fractional Brownian motion (FBM), yielding alternate derivations of known prediction results, along with some novel whitening and interpolation formulae. Some associated insights into the problem of discrete prediction are also explored. Closed-form expressions for the spectra and spectral factorization of the stationary processes associated with the FBM are obtained as part of this development.

Let Vk,n be the number of vertices of degree k in the Euclidean minimal spanning tree of Xi, , where the Xi are independent, absolutely continuous random variables with values in Rd. It is proved that n–1Vk,n converges with probability 1 to a constant α k,d. Intermediate results provide information about how the vertex degrees of a minimal spanning tree change as points are added or deleted, about the decomposition of minimal spanning trees into probabilistically similar trees, and about the mean and variance of Vk,n.