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Laws of the iterated logarithm for the central part of (semi-)stable measures on the Heisenberg groups

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Abstract

We prove laws of the iterated logarithm for certain symmetric stable and semistable measures on the Heisenberg groups.

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References

  1. Araujo, A., Giné, E.: The Central Limit Theorem for Real and Banach Valued Random Variables. New York: Wiley. 1980.

    Google Scholar 

  2. Chover, J.: A law of the iterated logarithm for stable summands. Proc. Amer. Math. Soc.17, 441–443 (1966).

    Google Scholar 

  3. Drisch, T., Gallardo, L.: Stable laws on the Heisenberg groups. In: Heyer, H., (ed.), Probability measures on groups VII. Lect. Notes Math.1064, 56–79. Berlin-Heidelberg-New York: Springer. 1984.

    Google Scholar 

  4. Hazod, W.: Stable probabilities on locally compact groups. In: Heyer, H., (ed.), Probability measures on groups. Lect Notes Math.928, 183–211, Berlin-Heidelberg-New York: Springer. 1982.

    Google Scholar 

  5. Hazod, W.: Stable probability measures on groups and on vector spaces. A survey. In: Heyer, H. (ed.), Probability measures on groups VIII. Lect. Notes Math.1210, 304–352, Berlin-Heidelberg-New York: Springer. 1986.

    Google Scholar 

  6. Heyde, C. C.: On large deviation problems for sums of random variables which are not attracted to the normal law. Ann. Math. Statist.38, 1575–1578 (1967).

    Google Scholar 

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

    Google Scholar 

  8. Hochschild, G.: The Structure of Lie Groups. San Francisco: Holden-Day, Inc. 1965.

    Google Scholar 

  9. Neuenschwander, D.: A gaussian central limit theorem for trimmed products on simply connected step 2-nilpotent Lie groups. J. Theoret. Probab.8(1), 165–171 (1995).

    Google Scholar 

  10. Scheffler, H. P.: A law of the iterated logarithm for stable laws on homogeneous groups. Preprint.

  11. Scheffler, H. P.: A law of the iterated logarithm for semistable laws on vector spaces and homogeneous groups. Preprint.

  12. Siebert, E.: Über die Erzeugung von Faltungshalbgruppen auf beliebigen lokalkompakten Gruppen. Math. Z.131, 313–333 (1973).

    Google Scholar 

  13. Siebert, E.: Fourier analysis and limit theorems for convolution semigroups on a locally compact group. Adv. in Math.29, 111–154 (1981).

    Google Scholar 

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Authors and Affiliations

  1. Ecole des Hautes Etudes Commercials Institut de Sciences Actuarielles, Université de Lausanne, CH-1015, Lausanne, Switzerland

    Daniel Neuenschwander

  2. Institut für Mathematik, Universität Dortmund, D-44221, Dortmund, Germany

    Hans-Peter Scheffler

Authors
  1. Daniel Neuenschwander
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  2. Hans-Peter Scheffler
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Neuenschwander, D., Scheffler, HP. Laws of the iterated logarithm for the central part of (semi-)stable measures on the Heisenberg groups. Monatshefte für Mathematik 121, 265–274 (1996). https://doi.org/10.1007/BF01298954

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  • DOI: https://doi.org/10.1007/BF01298954

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