Standard

Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet. / Tsilevich, Natalia; Vershik, Anatoly.

In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, Vol. 329, No. 2, 15.07.1999, p. 163-168.

Research output: Contribution to journal › Article › peer-review

Harvard

Tsilevich, N & Vershik, A 1999, 'Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet', Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, vol. 329, no. 2, pp. 163-168. https://doi.org/10.1016/S0764-4442(99)80482-0

APA

Tsilevich, N., & Vershik, A. (1999). Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet. Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, 329(2), 163-168. https://doi.org/10.1016/S0764-4442(99)80482-0

Vancouver

Tsilevich N, Vershik A. Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet. Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 1999 Jul 15;329(2):163-168. https://doi.org/10.1016/S0764-4442(99)80482-0

Author

Tsilevich, Natalia ; Vershik, Anatoly. / Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet. In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 1999 ; Vol. 329, No. 2. pp. 163-168.

BibTeX

@article{24870266239f4359bfaaef9e481502c1,
title = "Quasi-invariance du processus gamma et propri{\'e}t{\'e}s multiplicatives des distributions de Poisson-Dirichlet",
abstract = "In this paper we describe new fundamental properties of the law PΓ of the classical gamma process and related properties of the Poisson-Dirichlet measures PD(θ). We prove the quasi-invariance of the measure PΓ w ith respect to an infinite-dimensional multiplicative group (the fact first disc overed in [4]) and the Markov-Krein identity as corollaries of the formula for the Laplace transform of PΓ. The quasi-invariance of the measure P Γ allows us to obtain new quasi-invariance properties of the mea sure PD(θ). The corresponding invariance properties hold for σ-fini te analogues of PΓ and PD(θ). We also show that the meas ure PΓ can be considered as a limit of measures corresponding to the α-stable L{\'e}vy processes when the parameter α tends to zero. Our approach is based on considering simultaneously the gamma process (especiall y its Laplace transform) and its simplicial part - the Poisson-Dirichlet measures .",
author = "Natalia Tsilevich and Anatoly Vershik",
year = "1999",
month = jul,
day = "15",
doi = "10.1016/S0764-4442(99)80482-0",
language = "французский",
volume = "329",
pages = "163--168",
journal = "Comptes Rendus Mathematique",
issn = "1631-073X",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - Quasi-invariance du processus gamma et propriétés multiplicatives des distributions de Poisson-Dirichlet

AU - Tsilevich, Natalia

AU - Vershik, Anatoly

PY - 1999/7/15

Y1 - 1999/7/15

N2 - In this paper we describe new fundamental properties of the law PΓ of the classical gamma process and related properties of the Poisson-Dirichlet measures PD(θ). We prove the quasi-invariance of the measure PΓ w ith respect to an infinite-dimensional multiplicative group (the fact first disc overed in [4]) and the Markov-Krein identity as corollaries of the formula for the Laplace transform of PΓ. The quasi-invariance of the measure P Γ allows us to obtain new quasi-invariance properties of the mea sure PD(θ). The corresponding invariance properties hold for σ-fini te analogues of PΓ and PD(θ). We also show that the meas ure PΓ can be considered as a limit of measures corresponding to the α-stable Lévy processes when the parameter α tends to zero. Our approach is based on considering simultaneously the gamma process (especiall y its Laplace transform) and its simplicial part - the Poisson-Dirichlet measures .

AB - In this paper we describe new fundamental properties of the law PΓ of the classical gamma process and related properties of the Poisson-Dirichlet measures PD(θ). We prove the quasi-invariance of the measure PΓ w ith respect to an infinite-dimensional multiplicative group (the fact first disc overed in [4]) and the Markov-Krein identity as corollaries of the formula for the Laplace transform of PΓ. The quasi-invariance of the measure P Γ allows us to obtain new quasi-invariance properties of the mea sure PD(θ). The corresponding invariance properties hold for σ-fini te analogues of PΓ and PD(θ). We also show that the meas ure PΓ can be considered as a limit of measures corresponding to the α-stable Lévy processes when the parameter α tends to zero. Our approach is based on considering simultaneously the gamma process (especiall y its Laplace transform) and its simplicial part - the Poisson-Dirichlet measures .

UR - http://www.scopus.com/inward/record.url?scp=0033565164&partnerID=8YFLogxK

U2 - 10.1016/S0764-4442(99)80482-0

DO - 10.1016/S0764-4442(99)80482-0

M3 - статья

AN - SCOPUS:0033565164

VL - 329

SP - 163

EP - 168

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

IS - 2

ER -

ID: 49790388