Pre-limit Theorems and Their Applications
Source: Acta Applicandae Mathematicae, Volume 58, Number 1-3, September 1999 , pp. 159-174(16)
Abstract: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.
Document Type: Regular Paper
Affiliations: 1: St. Petersburg State University for Architecture and Civil Engineering, 2nd Krasnoarmeyskaya, 4, 198005 St. Petersburg, Russia. e-mail: email@example.com 2: Department of Economics, University of Karlsruhe, Postfach 6980, D-76128 Karlsruhe, Germany. e-mail: firstname.lastname@example.org 3: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403, USA. e-mail: email@example.com
Publication date: September 1, 1999