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The extended hypergeometric class of Lévy processes

Part of: Stochastic processes

Published online by Cambridge University Press:  30 March 2016

A. E. Kyprianou ,
J. C. Pardo  and
A. R. Watson
A. E. Kyprianou
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Email address: a.kyprianou@bath.ac.uk.
J. C. Pardo
Affiliation:
CIMAT, CIMAT, Calle Jalisco s/n, Mineral de Valenciana, 36240 Guanajuato, Mexico. Email address: jcpardo@cimat.mx.
A. R. Watson
Affiliation:
Department of Mathematics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland. Email address: alexander.watson@math.uzh.ch.
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Abstract

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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.

Keywords

Lévy processhypergeometric Lévy processextended hypergeometric Lévy processWiener-Hopf factorisationexponential functionalstable processpath-censored stable processconditioned stable processhitting distributionhitting probability

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 60G18: Self-similar processes 60G52: Stable processes
Type
Part 8. Markov processes and renewal theory
Information
Journal of Applied Probability , Volume 51 , Issue A: Celebrating 50 Years of The Applied Probability Trust , December 2014 , pp. 391 - 408
Copyright
Copyright © Applied Probability Trust 2014 

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