Multiresolution Gaussian Processes

Multiresolution Gaussian Processes Supplementary Material

Meaningful MRA initialization for discrete time series

Though frequently and commonly applied to discrete-time processes, the discrete wavelet transform is de"ned only for, and should therefore strictly speaking be applied only to, continuous-time processes. We provide a method for applying it to intrinsically discrete data, in such a way that the spectrum of discrete second-order processes can be meaningfully studied. The practical step required i...

The Rate of Entropy for Gaussian Processes

In this paper, we show that in order to obtain the Tsallis entropy rate for stochastic processes, we can use the limit of conditional entropy, as it was done for the case of Shannon and Renyi entropy rates. Using that we can obtain Tsallis entropy rate for stationary Gaussian processes. Finally, we derive the relation between Renyi, Shannon and Tsallis entropy rates for stationary Gaussian proc...

The Modeling and Estimation of Statistically Self-Similar Processes in a Multiresolution Framework

Statistically self-similar (SSS) processes can be used to describe a variety of physical phenomena, yet modeling these phenomena has proved challenging. Most of the proposed models for SSS and approximately SSS processes have power spectra that behave as 1=f , such as fractional Brownian motion (fBm), fractionally differenced noise, and wavelet-based syntheses. The most flexible framework is pe...

Complete convergence of moving-average processes under negative dependence sub-Gaussian assumptions

The complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. As a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.