The Doob–McKean Identity for Stable Lévy Processes

Andreas E. Kyprianou; Neil O’Connell

doi:10.1007/978-3-030-83309-1_15

The Doob–McKean Identity for Stable Lévy Processes

Andreas E. Kyprianou, Neil O’Connell

University College Dublin

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

4 Citations (SciVal)

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.

Original language	English
Title of host publication	A Lifetime of Excursions Through Random Walks and Lévy Processes
Editors	L. Chaumont, A. E. Kyprianou
Place of Publication	Cham, Switzerland
Publisher	Birkhäuser
Pages	269-282
Number of pages	14
ISBN (Electronic)	9783030833091
ISBN (Print)	9783030833084
DOIs	https://doi.org/10.1007/978-3-030-83309-1_15
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

Bibliographical note

Funding Information:
Research supported by the European Research Council (Grant No. 669306).

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.

Keywords

Cauchy Processes
Doob h-transform
Radial process

ASJC Scopus subject areas

Statistics and Probability
Applied Mathematics
Mathematical Physics
Mathematics (miscellaneous)

Access to Document

10.1007/978-3-030-83309-1_15

Cite this

The Doob–McKean Identity for Stable Lévy Processes. / Kyprianou, Andreas E.; O’Connell, Neil.
A Lifetime of Excursions Through Random Walks and Lévy Processes . ed. / L. Chaumont; A. E. Kyprianou . Cham, Switzerland: Birkhäuser, 2021. p. 269-282 (Progress in Probability; Vol. 78).

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

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AB - 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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KW - Radial process

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ER -

The Doob–McKean Identity for Stable Lévy Processes

Abstract

Publication series

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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