Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of W. Doeblin

W. Hazod

Annales de l'I.H.P. Probabilités et statistiques (1993)

  • Volume: 29, Issue: 3, page 339-355
  • ISSN: 0246-0203

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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 29.3 (1993): 339-355. <http://eudml.org/doc/77461>.

@article{Hazod1993,
author = {Hazod, W.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {probability distribution; convolution semigroup; locally compact group; infinitely divisible measures; contractible groups},
language = {eng},
number = {3},
pages = {339-355},
publisher = {Gauthier-Villars},
title = {Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of W. Doeblin},
url = {http://eudml.org/doc/77461},
volume = {29},
year = {1993},
}

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
PB - Gauthier-Villars
VL - 29
IS - 3
SP - 339
EP - 355
LA - eng
KW - probability distribution; convolution semigroup; locally compact group; infinitely divisible measures; contractible groups
UR - http://eudml.org/doc/77461
ER -

References

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  3. [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. Zbl0063.01128MR5541
  4. [F] W. Feller, An Introduction to Probability Theory and its Applications, vol. II, 2nd. Ed., J. Wiley & Sons, New York-London, 1971. Zbl0219.60003
  5. [Ha] W. Hazod, Stetige Faltungshalbgruppen von Wahrscheinlichkeitsmaßen und erzeugende Distributionen, Lecture Notes in Mathematics595, Springer, 1977. Zbl0373.60010MR488208
  6. [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. Zbl0789.60007MR1201063
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  8. [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. Zbl0821.60009MR1178987
  9. [M-R] P.R. Müller-Römer, Kontrahierbare Erweiterungen kontrahierbarer Gruppen, J. Reine Angew. Math., Vol. 283/284, 1976, pp. 238-264. Zbl0341.43003MR407194
  10. [No1] S. Nobel, Grenzwertsätze für Wahrscheinlichkeitsmaße auf einfach zusammenhängenden nilpotenten Liegruppen, Dissertation Universität Dortmund, 1988. Zbl0692.60006
  11. [No2] S. Nobel, Limit Theorems for Probability Measures on Simply Connected Nilpotent Lie Groups, J. Th. Probability, Vol. 4, 1991, pp. 261-284. Zbl0722.60011MR1100234
  12. [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. Zbl0459.60016MR625342
  13. [S] Riddi Shah, Infinitely Divisible Measures on p-adic Groups, J. Th. Probability, Vol. 4, 1991, pp. 391-406. Zbl0725.60011MR1100241
  14. [Si1] E. Siebert, Fourier Analysis and Limit Theorems for Convolution Semigroups on a Locally Compact Group, Adv. Math., Vol. 39, 1981, pp. 111-154. Zbl0469.60014MR609202
  15. [Si2] E. Siebert, Einbettung unendlich teilbarer Wahrscheinlichkeitsmaße auf topologischen Gruppen. Z. Wahrscheinlichkeitstheorie verw. Gebiete, Vol. 28, 1974, pp. 227-247. Zbl0264.60004MR362434
  16. [Si3] E. Siebert, Contractive Automorphisms on Locally Compact Groups, Math. Z., Vol. 191, 1986, pp. 73-90. Zbl0562.22002MR812604
  17. [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. Zbl0699.22002MR1020538
  18. [Th] Nguyen Van Thu, A New Version of Doeblin's Theorem, Bull. Acad. Pol. Sci. Ser. Sci. Math., Vol. 29, 1981, pp. 643-648. Zbl0499.60004MR654227

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