Wavelet methods to study the pointwise regularity of the generalized Rosenblatt process

TL;DR

This paper uses wavelet techniques to analyze the pointwise regularity of the generalized Rosenblatt process, extending known results from Gaussian to non-Gaussian processes and identifying three distinct regularity behaviors.

Contribution

It introduces wavelet-based methods to characterize the pointwise regularity of the Rosenblatt process, extending prior Gaussian results to a non-Gaussian setting.

Findings

Identification of three types of pointwise regularity behaviors.

Development of fine bounds on process increments.

Extension of regularity results from Gaussian to non-Gaussian processes.

Abstract

We prove that we can identify three types of pointwise behaviour in the regularity of the (generalized) Rosenblatt process. This extends to a non Gaussian setting previous results known for the (fractional) Brownian motion. On this purpose, fine bounds on the increments of the Rosenblatt process are needed. Our analysis is essentially based on various wavelet methods.