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Double hypergeometric Lévy processes and self-similarity

Part of: Stochastic processes

Published online by Cambridge University Press:  25 February 2021

Andreas E. Kyprianou ,
Juan Carlos Pardo  and
Matija Vidmar Open the ORCID record for Matija Vidmar [Opens in a new window]
Andreas E. Kyprianou*
Affiliation:
University of Bath
Juan Carlos Pardo*
Affiliation:
Centro de Investigación en Matemáticas
Matija Vidmar*
Affiliation:
University of Ljubljana
*
*Postal address: Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom. Email: a.kyprianou@bath.ac.uk
**Postal address: Centro de Investigación en Matemáticas, Apartado Postal 402, CP 36000, Calle Jalisco s/n, Mineral de Valencianam Guanajuato, Gto. Mexico. Email: jcpardo@cimat.mx
***Postal address: Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 21, 1000 Ljubljana, Slovenia. Email: matija.vidmar@fmf.uni-lj.si
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Abstract

Motivated by a recent paper (Budd (2018)), where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of Lévy processes, called the double hypergeometric class, whose Wiener–Hopf factorisation is explicit, and as a result many functionals can be determined in closed form.

Keywords

Lévy processesWiener–Hopf factorisationself-similar Markov processescomplete Bernstein functionsPick functions

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 60G18: Self-similar processes 60G52: Stable processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 58 , Issue 1 , March 2021 , pp. 254 - 273
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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