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Contents of PMS, Vol. 29, Fasc. 2,
pages 181 - 204
 

A FAMILY OF GENERALIZED GAMMA CONVOLUTED VARIABLES

B. Roynette
P. Vallois
M. Yor

Abstract: a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description to prove that several r.v.’s, related to the length of excursions away from 0 for a recurrent linear diffusion on R + , are GGC. Finally, in the third part, we apply our results to the case of Bessel processes with dimension d = 2(1 - a) , where 0 < d < 2 or 0 < a < 1 .

2000 AMS Mathematics Subject Classification: 60J25, 60G51, 60E07, 60E05.

Keywords and phrases: GGC variables, lengths of excursions, Bessel processes.

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