@inbook{db57803a59fe4cb5aa8b08f0a8f9bd20,
title = "The Doob–McKean Identity for Stable L{\'e}vy Processes",
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.",
keywords = "Cauchy Processes, Doob h-transform, Radial process",
author = "Kyprianou, {Andreas E.} and Neil O{\textquoteright}Connell",
note = "Funding Information: Research supported by the European Research Council (Grant No. 669306). Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",
year = "2021",
month = jul,
day = "30",
doi = "10.1007/978-3-030-83309-1_15",
language = "English",
isbn = "9783030833084",
series = "Progress in Probability",
publisher = "Birkhauser",
pages = "269--282",
editor = "L. Chaumont and {Kyprianou }, {A. E.}",
booktitle = "A Lifetime of Excursions Through Random Walks and L{\'e}vy Processes",
}