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More on hypergeometric Lévy processes

Part of: Stochastic processes General theory of linear operators

Published online by Cambridge University Press:  25 July 2016

Emma L. Horton  and
Andreas E. Kyprianou
Emma L. Horton*
Affiliation:
University of Bath
Andreas E. Kyprianou*
Affiliation:
University of Bath
*
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK. Email address: elh48@bath.ac.uk
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK. Email address: a.kyprianou@bath.ac.uk
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Abstract

Kuznetsov and co-authors in 2011‒14 introduced the family of hypergeometric Lévy processes. They appear naturally in the study of fluctuations of stable processes when one analyses stable processes through the theory of positive self-similar Markov processes. Hypergeometric Lévy processes are defined through their characteristic exponent, which, as a complex-valued function, has four independent parameters. In 2014 it was shown that the definition of a hypergeometric Lévy process could be taken to include a greater range of the aforesaid parameters than originally specified. In this short article, we push the parameter range even further.

Keywords

Hypergeometric Lévy processWiener‒Hopf factorisationstable processself-similar Markov process

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60G18: Self-similar processes 60G52: Stable processes 47A68: Factorization theory (including Wiener-Hopf and spectral factorizations)
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 153 - 158
Copyright
Copyright © Applied Probability Trust 2016 

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References

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