Tilted stable subordinators, Gamma time changes and Occupation Time of rays by Bessel Spiders

We exhibit, in the form of some identities in law, some connections between tilted stable subordinators, time-changed by independent Gamma processes and the occupation times of Bessel spiders, or their bridges. These identities in law are then explained thanks to excursion theory.

[1]  L. Chaumont,et al.  Exercises in probability. A guided tour from measure theory to random processes, via conditioning. Second edition , 2012 .

[2]  P. Salminen,et al.  On the excursion theory for linear diffusions , 2006, math/0612687.

[3]  Jim Pitman,et al.  Une extension multidimensionnelle de la loi de l'arc sinus , 1989 .

[4]  Lennart Bondesson,et al.  Generalized Gamma Convolutions and Related Classes of Distributions and Densities , 1992 .

[5]  M. Yor,et al.  On a particular class of self-decomposable random variables: the durations of Bessel excursions straddling independent exponential times , 2006 .

[6]  Luc Devroye,et al.  A NOTE ON LINNIK'S DISTRIBUTION , 1990 .

[7]  Thierry Huillet,et al.  On Linnik's continuous-time random walks , 2000 .

[8]  Eugenio Melilli,et al.  Some new results for dirichlet priors , 2000 .

[9]  Luc Devroye.  Random variate generation in one line of code , 1996, Winter Simulation Conference.

[10]  Olof Thorin,et al.  On the infinite divisibility of the lognormal distribution , 1977 .

[11]  Lancelot F. James.  Gamma Tilting Calculus for GGC and Dirichlet means with applications to Linnik processes and Occupation Time Laws for Randomly Skewed Bessel Processes and Bridges , 2006 .

[12]  Infinitely Divisible Distributions and Bessel Functions Associated with Random Walks , 1966 .

[13]  John Lamperti,et al.  An occupation time theorem for a class of stochastic processes , 1958 .

[14]  M. Yor,et al.  On constants related to the choice of the local time at 0, and the corresponding Itô measure for Bessel processes with dimension d = 2(1 − α ), 0 < α < 1 , 2008 .