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A family of generalized gamma convoluted variables

Roynette R., Vallois P., Yor M.

Probability and Mathematical Statistics

2009

Vol. 29, Fasc. 2

181--204

This paper consists of three parts: in the first part, we describe 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 − α), where 0 < d < 2 or 0 < α< 1.