A NEW IDEAL METRIC WITH APPLICATIONS TO MULTIVARIATE STABLE LIMIT-THEOREMS

• 成果类型: Article
• 署名作者: RACHEV, ST; RUSCHENDORF, L
• 署名单位: University of Munster
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01192443
• 发表日期: 1992
• 页码: 163-187
• 关键词: independent random-variables; distributions; sums; approximation; CONVERGENCE

摘要

A new ideal metric of order r > 1 is introduced on R(k) 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-Esseen type result in the stable case, obtain the limiting behaviour of multivariate summability methods and discuss the approximation problem by compound Poisson distributions.