# Double hypergeometric L\'evy processes and self-similarity

## TL;DR

This paper introduces the double hypergeometric class of Lévy processes, which have explicit Wiener-Hopf factorisation, enabling closed-form solutions for various functionals, inspired by recent developments in self-similar Markov processes.

## Contribution

It presents a new family of Lévy processes with explicit Wiener-Hopf factorisation, expanding the analytical tools for studying self-similar processes.

## Key findings

- Explicit Wiener-Hopf factorisation for the new Lévy class
- Closed-form expressions for key functionals
- Connection to self-similar Markov processes

## Abstract

Motivated by a recent paper of Budd, where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of L\'evy processes, called the double hypergeometric class, whose Wiener-Hopf factorisation is explicit, and as a result many functionals can be determined in closed form.