Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of W. Doeblin
Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) no. 3, pp. 339-355.
@article{AIHPB_1993__29_3_339_0,
     author = {Hazod, W.},
     title = {Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of {W.} {Doeblin}},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {339--355},
     publisher = {Gauthier-Villars},
     volume = {29},
     number = {3},
     year = {1993},
     mrnumber = {1246638},
     zbl = {0812.60013},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1993__29_3_339_0/}
}
TY  - JOUR
AU  - Hazod, W.
TI  - Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of W. Doeblin
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1993
SP  - 339
EP  - 355
VL  - 29
IS  - 3
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1993__29_3_339_0/
LA  - en
ID  - AIHPB_1993__29_3_339_0
ER  - 
%0 Journal Article
%A Hazod, W.
%T Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of W. Doeblin
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1993
%P 339-355
%V 29
%N 3
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1993__29_3_339_0/
%G en
%F AIHPB_1993__29_3_339_0
Hazod, W. Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of W. Doeblin. Annales de l'I.H.P. Probabilités et statistiques, Tome 29 (1993) no. 3, pp. 339-355. http://www.numdam.org/item/AIHPB_1993__29_3_339_0/

[Ba1] J. Barańska, Universal Doeblin Distributions in a Hilbert Space, Bull. Acad. Pol. Sci., Vol. 26, 1977, pp. 343-346. | MR | Zbl

[Ba2] J. Baránska, Domain of Partial Attraction for Infinitely Divisible Distributions in a Hilbert Space, Coll. Math., Vol. 28, 1973, pp. 317-322. | EuDML | MR | Zbl

[Doe] W. Doeblin, Sur l'ensemble de puissances d'une loi de probabilité, Studia Math., Vol. 9, 1940, pp. 71-96; Reprint: Ann. E. Norm. Sup. Vol. 63, 1947, pp. 317-350. | EuDML | JFM | Numdam | MR | Zbl

[F] W. Feller, An Introduction to Probability Theory and its Applications, vol. II, 2nd. Ed., J. Wiley & Sons, New York-London, 1971.

[Ha] W. Hazod, Stetige Faltungshalbgruppen von Wahrscheinlichkeitsmaßen und erzeugende Distributionen, Lecture Notes in Mathematics 595, Springer, 1977. | MR | Zbl

[H-S] W. Hazod and H.P. Scheffler, The Domains of Partial Attraction of Probabilities on Groups and on Vector Spaces, J. Th. Probability, Vol. 6, 1993, pp. 175-186. | MR | Zbl

[He] H. Heyer, Probability Measures on Locally Compact Groups, Berlin-Heidelberg- New York, Springer, 1977. | MR | Zbl

[Kh] Yu. S. Khokhlov, The Domain of Normal Attraction of a Stable Probability Measure on a Nilpotent Group, in: Probability measures on groups X, Proceedings Oberwolfach, 1990, pp. 239-247, New York, London, Plenum, 1991. | MR | Zbl

[M-R] P.R. Müller-Römer, Kontrahierbare Erweiterungen kontrahierbarer Gruppen, J. Reine Angew. Math., Vol. 283/284, 1976, pp. 238-264. | EuDML | MR | Zbl

[No1] S. Nobel, Grenzwertsätze für Wahrscheinlichkeitsmaße auf einfach zusammenhängenden nilpotenten Liegruppen, Dissertation Universität Dortmund, 1988. | Zbl

[No2] S. Nobel, Limit Theorems for Probability Measures on Simply Connected Nilpotent Lie Groups, J. Th. Probability, Vol. 4, 1991, pp. 261-284. | MR | Zbl

[Ph] Ho Dang Phuc, Universal Distributions for Infinitely Divisible Distributions on Fréchet Spaces, Ann. I. H. Poincaré, Sect. B., Vol. 17, 1981, pp. 219-227. | EuDML | Numdam | MR | Zbl

[S] Riddi Shah, Infinitely Divisible Measures on p-adic Groups, J. Th. Probability, Vol. 4, 1991, pp. 391-406. | MR | Zbl

[Si1] E. Siebert, Fourier Analysis and Limit Theorems for Convolution Semigroups on a Locally Compact Group, Adv. Math., Vol. 39, 1981, pp. 111-154. | MR | Zbl

[Si2] E. Siebert, Einbettung unendlich teilbarer Wahrscheinlichkeitsmaße auf topologischen Gruppen. Z. Wahrscheinlichkeitstheorie verw. Gebiete, Vol. 28, 1974, pp. 227-247. | MR | Zbl

[Si3] E. Siebert, Contractive Automorphisms on Locally Compact Groups, Math. Z., Vol. 191, 1986, pp. 73-90. | EuDML | MR | Zbl

[Si4] E. Siebert, Semistable Convolution Semigroups and the Topology of Contraction Groups, in: Probability Measures on groups IX, Oberwolfach, 1988, Lecture Notes Math. 1979, Springer, 1989. | MR | Zbl

[Th] Nguyen Van Thu, A New Version of Doeblin's Theorem, Bull. Acad. Pol. Sci. Ser. Sci. Math., Vol. 29, 1981, pp. 643-648. | MR | Zbl