Uniform convergence of compactly supported wavelet expansions of Gaussian random processes

TL;DR

This paper establishes new uniform convergence results in probability for Gaussian process expansions using compactly supported wavelets, applicable to nonstationary and stationary processes, with an exponential convergence rate.

Contribution

It provides the first uniform convergence in probability results for wavelet expansions of Gaussian processes, including nonstationary cases, with an exponential convergence rate.

Findings

Uniform convergence in probability established for wavelet expansions

Results applicable to both nonstationary and stationary Gaussian processes

Convergence rate shown to be exponential

Abstract

New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of nonstationary processes. An application of the obtained results to stationary processes is also presented. It is shown that the convergence rate of the expansions is exponential.