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More on hypergeometric Lévy processes

Published online by Cambridge University Press:  25 July 2016

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: [email protected]
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK. Email address: [email protected]

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2016 

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References

[1] Bertoin, J. (1996).Lévy Processes(Camb. Tracts Math. 121).Cambridge University Press.Google Scholar
[2] Horton, E. L. and Kyprianou, A. E. (2015).More on hypergeometric Lévy processes. Preprint. Available at http://arxiv.org/abs/1509.02352v1.Google Scholar
[3] Kuznetsov, A. and Pardo, J. C. (2013).Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes.Acta Appl. Math. 123,113139.CrossRefGoogle Scholar
[4] Kuznetsov, A.,Kyprianou, A. E. and Pardo, J. C. (2012).Meromorphic Lévy processes and their fluctuation identities.Ann. Appl. Prob. 22,11011135.CrossRefGoogle Scholar
[5] Kuznetsov, A.,Kyprianou, A. E.,Pardo, J. C. and van Schaik, K. (2011).A Wiener‒Hopf Monte Carlo simulation technique for Lévy processes.Ann. Appl. Prob. 21,21712190.CrossRefGoogle Scholar
[6] Kyprianou, A. E. (2014).Fluctuations of Lévy Processes with Applications: Introductory Lectures,2nd edn.Springer,Berlin.CrossRefGoogle Scholar
[7] Kyprianou, A. E.,Pardo, J. C. and Watson, A. R. (2014).The extended hypergeometric class of Lévy processes. In Celebrating 50 Years of the Applied Probability Trust (J. Appl. Prob. Spec. Vol. 51A), eds S. Asmussen, P. Jagers, I. Molchanov and L. C. G. Rogers,Applied Probability Trust,Sheffield, pp. 391408.Google Scholar
[8] Vigon, V. (2002).Simplifiez vos Lévy en titillant la factorisation de Wiener‒Hopf. Doctoral Thesis, INSA de Rouen.Google Scholar