Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples

Details Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples

2007-08-29

arxiv.org/abs/0708.3932v2

Probability Surveys 2008, Vol. 5, 346-415

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-PS118 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of

Scientific paper

10.1214/07-PS118

In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution (:GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet processes.To a GGC variable, one may associate a unique Thorin measure. Let $G$ a positive r.v. and $\Gamma_t(G)$ (resp. $\Gamma_t(1/G))$ the Generalized Gamma Convolution with Thorin measure $t$-times the law of $G$ (resp. the law of $1/G$). In Section 2, we compare the laws of $\Gamma_t(G)$ and $\Gamma_t(1/G)$.In Section 3, we present some old and some new examples of GGC variables, among which the lengths of excursions of Bessel processes straddling an independent exponential time.

Affiliated with

Also associated with

No associations

Rating

Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-240291