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On a particular class of self-decomposable random variables : the durations of Bessel excursions straddling independent exponential times

Bertoin J., Fujita T., Roynette B., Yor M.

Probability and Mathematical Statistics

2006

Vol. 26, Fasc. 2

315--366

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.