ON A PARTICULAR CLASS OF SELF-DECOMPOSABLE RANDOM
VARIABLES: THE DURATIONS OF BESSEL EXCURSIONS STRADDLING
INDEPENDENT EXPONENTIAL TIMES

J. Bertoin

T. Fujita

B. Roynette

M. Yor

Abstract: The distributional properties of the duration of a recurrent Bessel process straddling
an independent exponential time are studied in detail. Although our study may be
considered as a particular case of Winkel’s in [25], the infinite divisibility structure of
these Bessel durations is particularly rich and we develop algebraic properties for a
family of random variables arising from the Lévy measures of these durations.

2000 AMS Mathematics Subject Classification: 60E07, 60G15, 60J25, 60J55.

Key words and phrases: Bessel processes, self-decomposability, beta-gamma algebra,
general gamma convolutions.