The suprema of selector processes with the application to positive infinitely divisible processes

TL;DR

This paper offers a new proof for the expected supremum bounds of positive selector and empirical processes and extends these results to positive infinitely divisible processes, broadening their applicability.

Contribution

It presents an alternative proof and extends supremum bounds to positive infinitely divisible processes, advancing the theoretical understanding of these stochastic processes.

Findings

Alternative proof of supremum bounds for positive selector processes

Extension of bounds to positive infinitely divisible processes

Broader applicability of supremum estimates in stochastic process theory

Abstract

We provide an alternative proof of the recent result by Park and Pham (2022) on the expected suprema of positive selector and empirical processes. We extend it to positive infinitely divisible processes.