Suprema of canonical Weibull processes

TL;DR

This paper develops a method to bound the supremum of canonical processes with Weibull-like tail distributions, using non-increasing rearrangement to achieve two-sided bounds.

Contribution

It introduces a novel approach employing non-increasing rearrangement for bounding suprema of processes with Weibull tail distributions, extending existing techniques.

Findings

Provides two-sided bounds for suprema of Weibull-tailed processes

Uses non-increasing rearrangement method effectively

Extends understanding of tail behavior in canonical processes

Abstract

In this note we investigate the problem of bounding the suprema of canonical processes based on r.v.s with tails $\exp{(-t^r)}$, where $0<r \le 1$. We propose a method using non-increasing rearrangement that provides a two-sided bound.