The Doob–McKean Identity for Stable Lévy Processes

Andreas E. Kyprianou, Neil O’Connell

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


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 languageEnglish
Title of host publicationA Lifetime of Excursions Through Random Walks and Lévy Processes
EditorsL. Chaumont, A. E. Kyprianou
Place of PublicationCham, Switzerland
Number of pages14
ISBN (Electronic)9783030833091
ISBN (Print)9783030833084
Publication statusE-pub ahead of print - 30 Jul 2021

Publication series

NameProgress in Probability
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.


  • Cauchy Processes
  • Doob h-transform
  • Radial process

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics
  • Mathematical Physics
  • Mathematics (miscellaneous)


Dive into the research topics of 'The Doob–McKean Identity for Stable Lévy Processes'. Together they form a unique fingerprint.

Cite this