Pre-limit Theorems and Their Applications

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

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish
Pages (from-to)159-174
Number of pages16
JournalActa Applicandae Mathematicae
Issue number1-3
StatePublished - 1999


  • Prelimiting behavior
  • Random stability
  • Stable distribution


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