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Double hypergeometric Lévy processes and self-similarity

Published online by Cambridge University Press:  25 February 2021

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

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.

Type
Research Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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