The extended hypergeometric class of Lévy processes

Abstract

With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener-Hopf factorisation of a process in the extended class, and characterise its exponential functional. Finally, we give three concrete examples arising from transformations of stable processes.

22 pages

References in corpus (9)

• Wiener-Hopf factorization and distribution of extrema for a family of Lévy processes
• A Wiener--Hopf Monte Carlo simulation technique for Lévy processes
• Recurrent extensions of self-similar Markov processes and Cramér's condition II
• The Lamperti representation of real-valued self-similar Markov processes
• The hitting time of zero for a stable process
• Hitting distributions of alpha-stable processes via path censoring and self-similarity
• On the Lamperti stable processes
• Special, conjugate and complete scale functions for spectrally negative Lévy processes
• Explicit identities for Lévy processes associated to symmetric stable processes

Cited by in corpus (2)

• The uniqueness of the Wiener-Hopf factorisation of Lévy processes and random walks
• Markov additive friendships