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More on hypergeometric Lévy processes

  • Emma L. Horton (a1) and Andreas E. Kyprianou (a1)

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.

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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

References

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[1] Bertoin, J. (1996).Lévy Processes(Camb. Tracts Math. 121).Cambridge University Press.
[2] Horton, E. L. and Kyprianou, A. E. (2015).More on hypergeometric Lévy processes. Preprint. Available at http://arxiv.org/abs/1509.02352v1.
[3] Kuznetsov, A. and Pardo, J. C. (2013).Fluctuations of stable processes and exponential functionals of hypergeometric Lévy processes.Acta Appl. Math. 123,113139.
[4] Kuznetsov, A.,Kyprianou, A. E. and Pardo, J. C. (2012).Meromorphic Lévy processes and their fluctuation identities.Ann. Appl. Prob. 22,11011135.
[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.
[6] Kyprianou, A. E. (2014).Fluctuations of Lévy Processes with Applications: Introductory Lectures,2nd edn.Springer,Berlin.
[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.
[8] Vigon, V. (2002).Simplifiez vos Lévy en titillant la factorisation de Wiener‒Hopf. Doctoral Thesis, INSA de Rouen.

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More on hypergeometric Lévy processes

  • Emma L. Horton (a1) and Andreas E. Kyprianou (a1)

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