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A Lifetime of Excursions Through Random Walks and Lévy Processes Read chapter Read first chapter

2021 | OriginalPaper | Chapter

A Transformation for Spectrally Negative Lévy Processes and Applications

Authors : Marie Chazal, Andreas E. Kyprianou, Pierre Patie

Published in: A Lifetime of Excursions Through Random Walks and Lévy Processes

Publisher: Springer International Publishing

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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.

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previous chapter Some New Classes and Techniques in the Theory of Bernstein Functions
next chapter First-Passage Times for Random Walks in the Triangular Array Setting
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Metadata
Title
A Transformation for Spectrally Negative Lévy Processes and Applications
Authors
Marie Chazal
Andreas E. Kyprianou
Pierre Patie
Copyright Year
2021
Book
A Lifetime of Excursions Through Random Walks and Lévy Processes

Print ISBN: 978-3-030-83308-4

Electronic ISBN: 978-3-030-83309-1

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-83309-1_9