Journal of Applied Probability

The extended hypergeometric class of Lévy processes

A. E. Kyprianou, J. C. Pardo, and A. R. Watson

Abstract

We review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo (2013) with a view to computing fluctuation identities related to stable processes. We give the Wiener-Hopf factorisation of a process in the extended class, characterise its exponential functional, and give three concrete examples arising from transformations of stable processes.

Article information

Source
J. Appl. Probab. Volume 51A (2014), 391-408.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528488

Digital Object Identifier
doi:10.1239/jap/1417528488

Mathematical Reviews number (MathSciNet)
MR3317371

Subjects
Primary: 60G51: Processes with independent increments; Lévy processes 60G18: Self-similar processes 60G52: Stable processes

Keywords
Lévy process hypergeometric Lévy process extended hypergeometric Lévy process Wiener-Hopf factorisation exponential functional stable process path-censored stable process conditioned stable process hitting distribution hitting probability

Citation

Kyprianou, A. E.; Pardo, J. C.; Watson, A. R. The extended hypergeometric class of Lévy processes. J. Appl. Probab. 51A (2014), 391--408. doi:10.1239/jap/1417528488. https://projecteuclid.org/euclid.jap/1417528488.


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