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Contents of PMS, Vol. 26, Fasc. 2,
pages 315 - 366
 

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.

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