The suprema of infinitely divisible processes

TL;DR

This paper fully characterizes the expected suprema of infinitely divisible processes, removing previous technical assumptions and confirming a conjecture by M. Talagrand, advancing understanding in stochastic process theory.

Contribution

It provides a complete characterization of expected suprema for infinitely divisible processes, eliminating the $H(C_{0}, ext{delta})$ condition and proving Talagrand's conjecture.

Findings

Removed the $H(C_{0}, ext{delta})$ assumption

Settled Talagrand's conjecture

Enhanced understanding of infinitely divisible processes

Abstract

In this paper we complete the full characterization of the expected suprema of infinitely divisible processes. In particular, we remove the technical assumption called $H(C_{0},\delta)$ condition and settle positively the conjecture posed by M. Talagrand.