Acta Applicandae Mathematica

, Volume 58, Issue 1–3, pp 159–174 | Cite as

Pre-limit Theorems and Their Applications

  • L. B. Klebanov
  • S. T. Rachev
  • G. J. Szekely


There exists a considerable debate in the literature about the applicability of α-stable distributions as they appear in Lévy"s central limit theorems. A serious drawback of Lévy"s approach is that, in practice, one can never know whether the underlying distribution is heavy tailed, or just has a long but truncated tail. Limit theorems for stable laws are not robust with respect to truncation of the tail or with respect to any change from 'light" to 'heavy" tail, or conversely. In this talk we provide a new 'pre-limiting" approach that helps overcome this drawback of Lévy-type central limit theorems.

prelimiting behavior stable distribution random stability 


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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • L. B. Klebanov
    • 1
  • S. T. Rachev
    • 2
  • G. J. Szekely
    • 3
  1. 1.St. Petersburg State University for Architecture and Civil EngineeringSt. PetersburgRussia. e-mail
  2. 2.Department of EconomicsUniversity of KarlsruheKarlsruheGermany. e-mail
  3. 3.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA. e-mail

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