The extended hypergeometric class of Lévy processes.

A. E. Kyprianou; J. C. Pardo; A. R. Watson

doi:10.1239/jap/1417528488

The extended hypergeometric class of Lévy processes.

A. E. Kyprianou
, J. C. Pardo
, A. R. Watson

The University of Manchester

Research output: Contribution to journal › Article › peer-review

Abstract

Abstract: With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener–Hopf factorisation of a process in the extended class, and characterise its exponential functional. Finally, we give three concrete examples arising from transformations of stable processes.

Original language	English
Pages (from-to)	391-408
Number of pages	17
Journal	Journal of Applied Probability
Volume	51A
DOIs	https://doi.org/10.1239/jap/1417528488
Publication status	Published - 2014

Keywords

Levy process
hypergeometric Levy process
extended hypergeometric Levy process
Wiener-Hopf factorisation
exponential functional
stable process
path-censored stable process
conditioned stable process
hitting distribution
hitting probability

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10.1239/jap/1417528488

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title = "The extended hypergeometric class of L{\'e}vy processes.",

abstract = "Abstract: With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric L{\'e}vy processes explored in Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener–Hopf factorisation of a process in the extended class, and characterise its exponential functional. Finally, we give three concrete examples arising from transformations of stable processes.",

keywords = "Levy process, hypergeometric Levy process, extended hypergeometric Levy process, Wiener-Hopf factorisation, exponential functional, stable process, path-censored stable process, conditioned stable process, hitting distribution, hitting probability",

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year = "2014",

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language = "English",

volume = "51A",

pages = "391--408",

journal = "Journal of Applied Probability",

publisher = "Cambridge University Press",

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TY - JOUR

T1 - The extended hypergeometric class of Lévy processes.

AU - Kyprianou, A. E.

AU - Pardo, J. C.

AU - Watson, A. R.

PY - 2014

Y1 - 2014

N2 - Abstract: With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener–Hopf factorisation of a process in the extended class, and characterise its exponential functional. Finally, we give three concrete examples arising from transformations of stable processes.

AB - Abstract: With a view to computing fluctuation identities related to stable processes, we review and extend the class of hypergeometric Lévy processes explored in Kuznetsov and Pardo (arXiv:1012.0817). We give the Wiener–Hopf factorisation of a process in the extended class, and characterise its exponential functional. Finally, we give three concrete examples arising from transformations of stable processes.

KW - Levy process

KW - hypergeometric Levy process

KW - extended hypergeometric Levy process

KW - Wiener-Hopf factorisation

KW - exponential functional

KW - stable process

KW - path-censored stable process

KW - conditioned stable process

KW - hitting distribution

KW - hitting probability

U2 - 10.1239/jap/1417528488

DO - 10.1239/jap/1417528488

M3 - Article

VL - 51A

SP - 391

EP - 408

JO - Journal of Applied Probability

JF - Journal of Applied Probability

ER -

The extended hypergeometric class of Lévy processes.

Abstract

Keywords

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