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The Lévy-Khinchin Representation of the One Class of Signed Stable Measures and Some Its Applications

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Abstract

We study properties of symmetric stable measures with index α∈(2,4)∪(4,6). Such measures are signed ones and hence they are not probability measures. For this class of measures we construct an analogy of the Lévy-Khinchin representation. We show that in some sense these signed measures are limit measures for sums of independent random variables.

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Authors and Affiliations

  1. St.-Petersburg State University, St.-Petersburg, Russia

    N. V. Smorodina & M. M. Faddeev

Authors
  1. N. V. Smorodina
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  2. M. M. Faddeev
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Correspondence to N. V. Smorodina.

Additional information

This paper was partly supported by DFG 436 RUS 113/823, NSh 638.2008.1. The second author was supported by Russian Foundation for Basic Research 06-01-00249a and INTAS 05-100000807883.

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Smorodina, N.V., Faddeev, M.M. The Lévy-Khinchin Representation of the One Class of Signed Stable Measures and Some Its Applications. Acta Appl Math 110, 1289–1308 (2010). https://doi.org/10.1007/s10440-009-9510-9

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  • DOI: https://doi.org/10.1007/s10440-009-9510-9

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