A Transformation for Spectrally Negative Lévy Processes and Applications

Marie Chazal; Andreas E. Kyprianou; Pierre Patie

doi:10.1007/978-3-030-83309-1_9

A Transformation for Spectrally Negative Lévy Processes and Applications

Marie Chazal, Andreas E. Kyprianou, Pierre Patie

Cornell University

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

1 Citation (SciVal)

Abstract

The aim of this work is to extend and study a family of transformations between Laplace exponents of Lévy processes which have been introduced recently in a variety of different contexts, Patie (Bull Sci Math 133(4):355–382, 2009; Bernoulli 17(2):814–826, 2011), Kyprianou and Patie (Ann Inst H Poincar’ Probab Statist 47(3):917–928, 2011), Gnedin (Regeneration in Random Combinatorial Structures. arXiv:0901.4444v1 [math.PR]), Patie and Savov (Electron J Probab 17(38):1–22, 2012), as well as in older work of Urbanik (Probab Math Statist 15:493–513, 1995). We show how some specific instances of this mapping prove to be useful for a variety of applications.

Original language	English
Title of host publication	A Lifetime of Excursions Through Random Walks and Lévy Processes
Editors	M. Chazal, A. E. Kyprianou, P. Patie
Place of Publication	Cham, Switzerland
Publisher	Birkhäuser
Pages	157-180
Number of pages	24
ISBN (Electronic)	9783030833091
ISBN (Print)	9783030833084
DOIs	https://doi.org/10.1007/978-3-030-83309-1_9
Publication status	E-pub ahead of print - 30 Jul 2021

Publication series

Name	Progress in Probability
Volume	78
ISSN (Print)	1050-6977
ISSN (Electronic)	2297-0428

Keywords

Exponential functional
Fluctuation theory
Hypergeometric function
Intertwining
Positive self-similar Markov process
Spectrally negative Lévy process

ASJC Scopus subject areas

Statistics and Probability
Applied Mathematics
Mathematical Physics
Mathematics (miscellaneous)

Access to Document

10.1007/978-3-030-83309-1_9

Cite this

Chazal, M., Kyprianou, A. E., & Patie, P. (2021). A Transformation for Spectrally Negative Lévy Processes and Applications. In M. Chazal, A. E. Kyprianou, & P. Patie (Eds.), A Lifetime of Excursions Through Random Walks and Lévy Processes (pp. 157-180). (Progress in Probability; Vol. 78). Birkhäuser. Advance online publication. https://doi.org/10.1007/978-3-030-83309-1_9

A Transformation for Spectrally Negative Lévy Processes and Applications. / Chazal, Marie; Kyprianou, Andreas E.; Patie, Pierre.
A Lifetime of Excursions Through Random Walks and Lévy Processes . ed. / M. Chazal; A. E. Kyprianou; P. Patie. Cham, Switzerland: Birkhäuser, 2021. p. 157-180 (Progress in Probability; Vol. 78).

Research output: Chapter or section in a book/report/conference proceeding › Chapter or section

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A Transformation for Spectrally Negative Lévy Processes and Applications

Abstract

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Keywords

ASJC Scopus subject areas

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