A new ideal metric with applications to multivariate stable limit theorems

S. T. Rachev, L. Rüschendorf

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

A new ideal metric of order r>1 is introduced on ℝk and a thorough analysis of its metric properties is given. In comparison to the known ideal metric of Zolotarev this new metric allows estimates from above by pseudo difference moments and thus allows applications to stable limit theorems. As applications we give the right order Berry-Esséen type result in the stable case, obtain the limiting behaviour of multivariate summability methods and discuss the approximation problem by compound Poisson distributions.

Original languageEnglish
Pages (from-to)163-187
Number of pages25
JournalProbability Theory and Related Fields
Volume94
Issue number2
DOIs
StatePublished - Jun 1992

Keywords

  • Mathematics Subject Classification (1991): 60F05, 60E15

Fingerprint Dive into the research topics of 'A new ideal metric with applications to multivariate stable limit theorems'. Together they form a unique fingerprint.

  • Cite this