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2 results

  • More on hypergeometric Lévy processes

  • Part of
  • Emma L. Horton, Andreas E. Kyprianou
  • Journal:
    Advances in Applied Probability / Volume 48 / Issue A / July 2016
    Published online by Cambridge University Press:
    25 July 2016, pp. 153-158
    Print publication:
    July 2016

  • 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.

  • The extended hypergeometric class of Lévy processes

  • Part of
  • A. E. Kyprianou, J. C. Pardo, A. R. Watson
  • Journal:
    Journal of Applied Probability / Volume 51 / Issue A / December 2014
    Published online by Cambridge University Press:
    30 March 2016, pp. 391-408
    Print publication:
    December 2014
    • Article
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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.