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Stable laws on the heisenberg groups

Part of the Lecture Notes in Mathematics book series (LNM,volume 1064)

Abstract

We determine the generating distributions of the full continuous convolution semigroups of probabilities on the Heisenberg groups which are stable in the sense of Hazod. We obtain a classification of the limit distributions on the Heisenberg groups for the case of identically distributed random variables without centering.

Keywords

  • Automorphism Group
  • Heisenberg Group
  • Closed Subgroup
  • Semi Group
  • Vector Group

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References

  1. P. Baldi: Lois stables sur les déplacements de Rd. In: Probability Measures on Groups. Lecture Notes Math. 706. Berlin-Heidelberg-New York: Springer 1979.

    CrossRef  Google Scholar 

  2. Q.L. Burrell, M. McCrudden: Infinitely divisible distributions on connected nilpotent Lie groups. J. London Math. Soc. 7, 584–588 (1974).

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. W. Hazod: Stable Probabilities on Locally Compact Groups. In: Probability Measures on Groups. Lecture Notes Math. 928. Berlin-Heidelberg-New York: Springer 1982.

    CrossRef  Google Scholar 

  4. W. Hazod: Remarks on (Semi-) stable Probabilities. In: Probability Measures on Groups. Lecture Notes Math. Berlin-Heidelberg-New York: Springer 1984.

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  5. H. Heyer: Probability Measures on Locally Compact Groups. Berlin-Heidelberg-New York: Springer 1977.

    CrossRef  MATH  Google Scholar 

  6. J.P. Holmes, W.N. Hudson, J.D. Mason: Operator Stable Laws: Multiple Exponents and Elliptical Symmetry. Annals Prob. 10, 602–612 (1982).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. W.N. Hudson: Operator-Stable Distributions and Stable Marginals. J. Multivariate Analysis 10, 26–37 (1980).

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. W.N. Hudson, J.D. Mason: Operator-Stable Laws. J. Multivariate Analysis 11, 434–447 (1981).

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. M. Sharpe: Operator-Stable Probability Measures on Vector Groups. Trans. Amer. Math. Soc. 136, 51–65 (1969).

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1984 Springer-Verlag

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Drisch, T., Gallardo, L. (1984). Stable laws on the heisenberg groups. In: Heyer, H. (eds) Probability Measures on Groups VII. Lecture Notes in Mathematics, vol 1064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073634

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  • DOI: https://doi.org/10.1007/BFb0073634

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13341-4

  • Online ISBN: 978-3-540-38874-6

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