Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures;Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 329, Issue 2, 1999, Pages 163-168

  Tsilevich, Natalia ^b   Vershik, Anatoly ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033565164     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0764-4442(99)80482-0     Document Type: Article

References (12)

1. Cifarelli D.M., Regazzini E., Some remarks on the distribution functions of means of a Dirichlet process, Ann. Statist. 18 (1990) 429-442.
2. Ferguson T.S., A Bayesian analysis of some nonparametric problems, The Ann. Statis. 1 (1973) 209-230.
3. Ferguson T.S., Klass M.J., A representation of independent increment processes without Gaussian components, The Ann. Math. Statis. 43 (1972) 1634-1643.
4. x connected with a unipotent subgroup, Funct. Anal. 17 (2) (1983) 80-82.
5. Gelfand I.M., Graev M.I., Vershik A.M., Models of representations of current groups, in: Representations of Lie Groups and Lie Algebras, A.A. Kirillov (Ed.), Akadémiai Kiadö, Budapest, 1985, pp. 121-179.
6. Kingman J.F.C., Random discrete distributions, J. Roy. Statis. Soc. B 37 (1975) 1-22.
7. Kingman J.F.C., Poisson Processes, Clarendon Press, Oxford, 1993.
8. Lifschits M., Invariant measures generated by random fields with independent values, Funct. Anal. 19 (4) (1983) 92-92.
9. Lukacs E., A characterization of gamma distribution, Ann. Math. Statis. 26 (1965) 319-324.
10. Pitman J., Yor M., The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator, Ann. Probab. 25 (1997) 855-900.
11. Vershik A.M., Multivalued mappings with invariant measure (polymorphisms) and Markov operators, Zapiski Nauchnyh Seminarov LOMI 72 (1977) 26-61.
12. Vershik A., Yor M., Multiplicativité du Processus Gamma et Étude Asymptotique des Lois Stables D'indice α, Lorsque α Tend Vers 0, Prépublication du Laboratoire de probabilités de l'Université Paris VI, # 289, 1995, pp. 1-10.