Double hypergeometric Lévy processes and self-similarity

Andreas Kyprianou; Juan Carlos Pardo; Matija Vidmar

doi:10.1017/jpr.2020.86

Double hypergeometric Lévy processes and self-similarity

Andreas Kyprianou, Juan Carlos Pardo, Matija Vidmar

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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.

Original language	English
Pages (from-to)	254-273
Number of pages	20
Journal	Journal of Applied Probability
Volume	58
Issue number	1
Early online date	25 Feb 2021
DOIs	https://doi.org/10.1017/jpr.2020.86
Publication status	Published - 31 Mar 2021

Keywords

Lévy processes
Pick functions
Wiener-Hopf factorisation
complete Bernstein functions
self-similar Markov processes

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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Cite this

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title = "Double hypergeometric L{\'e}vy processes and self-similarity",

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 L{\'e}vy processes, called the double hypergeometric class, whose Wiener-Hopf factorisation is explicit, and as a result many functionals can be determined in closed form.",

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AU - Pardo, Juan Carlos

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AB - 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.

KW - Lévy processes

KW - Pick functions

KW - Wiener-Hopf factorisation

KW - complete Bernstein functions

KW - self-similar Markov processes

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Double hypergeometric Lévy processes and self-similarity

Abstract

Keywords

ASJC Scopus subject areas

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Real-Valued Self-Similar Markov Processes and their Applications

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Double hypergeometric Lévy processes and self-similarity

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

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Real-Valued Self-Similar Markov Processes and their Applications

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