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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 M. Winkel's in [Wink], 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.doi:10.5167/uzh-78183 fatcat:ilawz44bwvfhfkcyqe7gpd3kxa