Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory

TL;DR

This paper investigates the asymptotic properties of wavelet coefficients in long-memory processes generated by nonlinear filtering of Gaussian inputs, revealing their non-Gaussian, self-similar nature in the limit.

Contribution

It provides a detailed analysis of the limiting behavior of wavelet coefficients for non-linear subordinated processes with long memory, extending understanding of their asymptotic distribution.

Findings

Wavelet coefficients converge to non-Gaussian limits in Wiener chaos.

The processes exhibit generalized self-similarity in the asymptotic regime.

Results apply to both stationary and non-stationary long-memory processes.

Abstract

We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that appear in the limit are random, typically non--Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.