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A Lifetime of Excursions Through Random Walks and Lévy ProcessesOn Doney’s Striking Factorization of the Arc-Sine Law

A Lifetime of Excursions Through Random Walks and Lévy Processes: On Doney’s Striking... [In Doney (Bull Lond Math Soc 19(2):177–182, 1987), R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximation. In this paper, we provide an alternative proof and a generalization of this factorization based on the theory recently developed for the exponential functional of Lévy processes. As a by-product, we provide some interesting distributional properties for these variables and also some new examples of the factorization of the arc-sine law.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Lifetime of Excursions Through Random Walks and Lévy ProcessesOn Doney’s Striking Factorization of the Arc-Sine Law

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References (35)

Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2021
ISBN
978-3-030-83308-4
Pages
43 –58
DOI
10.1007/978-3-030-83309-1_3
Publisher site
See Chapter on Publisher Site

Abstract

[In Doney (Bull Lond Math Soc 19(2):177–182, 1987), R. Doney identifies a striking factorization of the arc-sine law in terms of the suprema of two independent stable processes of the same index by an elegant random walks approximation. In this paper, we provide an alternative proof and a generalization of this factorization based on the theory recently developed for the exponential functional of Lévy processes. As a by-product, we provide some interesting distributional properties for these variables and also some new examples of the factorization of the arc-sine law.]

Published: Jul 30, 2021

Keywords: Lévy processes; arc-sine law; mellin transform; recurrence equation

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