L\'evy measures of infinitely divisible positive processes -- examples and distributional identities

TL;DR

This paper explores how the Le9vy measure characterizes positive infinitely divisible processes without drift, demonstrating that understanding these measures yields significant distributional identities even for simple cases.

Contribution

It shows that the Le9vy measure fully characterizes such processes and enables derivation of notable distributional identities, advancing theoretical understanding.

Findings

Le9vy measures determine the law of positive infinitely divisible processes without drift.

Distributional identities can be derived from Le9vy measures even in simple examples.

The results build on recent advances by the authors in the field.

Abstract

The law of a positive infinitely divisible process with no drift is characterized by its L\'evy measure on the paths space. Based on recent results of the two authors, it is shown that even for simple examples of such processes, the knowledge of their L\'evy measures allows to obtain remarkable distributional identities.