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

2021 | OriginalPaper | Chapter

The Doob–McKean Identity for Stable Lévy Processes

Authors : Andreas E. Kyprianou, Neil O’Connell

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

Publisher: Springer International Publishing

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Abstract

We re-examine the celebrated Doob–McKean identity that identifies a conditioned one-dimensional Brownian motion as the radial part of a 3-dimensional Brownian motion or, equivalently, a Bessel-3 process, albeit now in the analogous setting of isotropic α-stable processes. We find a natural analogue that matches the Brownian setting, with the role of the Brownian motion replaced by that of the isotropic α-stable process, providing one interprets the components of the original identity in the right way.

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previous chapter Slowly Varying Asymptotics for Signed Stochastic Difference Equations
next chapter Oscillatory Attraction and Repulsion from a Subset of the Unit Sphere or Hyperplane for Isotropic Stable Lévy Processes
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Metadata
Title
The Doob–McKean Identity for Stable Lévy Processes
Authors
Andreas E. Kyprianou
Neil O’Connell
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_15