A new ideal metric with applications to multivariate stable limit theorems

S. T. Rachev; L. Rüschendorf

doi:10.1007/BF01192443

A new ideal metric with applications to multivariate stable limit theorems

S. T. Rachev, L. Rüschendorf

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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-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 language	English
Pages (from-to)	163-187
Number of pages	25
Journal	Probability Theory and Related Fields
Volume	94
Issue number	2
DOIs	https://doi.org/10.1007/BF01192443
State	Published - Jun 1992

Keywords

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

Access to Document

10.1007/BF01192443

Cite this

@article{6c056c19f88a444897e9aeca40c645ad,

title = "A new ideal metric with applications to multivariate stable limit theorems",

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-Ess{\'e}en type result in the stable case, obtain the limiting behaviour of multivariate summability methods and discuss the approximation problem by compound Poisson distributions.",

keywords = "Mathematics Subject Classification (1991): 60F05, 60E15",

author = "Rachev, {S. T.} and L. R{\"u}schendorf",

year = "1992",

month = jun,

doi = "10.1007/BF01192443",

language = "English",

volume = "94",

pages = "163--187",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

number = "2",

}

TY - JOUR

T1 - A new ideal metric with applications to multivariate stable limit theorems

AU - Rachev, S. T.

AU - Rüschendorf, L.

PY - 1992/6

Y1 - 1992/6

N2 - 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.

AB - 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.

KW - Mathematics Subject Classification (1991): 60F05, 60E15

UR - http://www.scopus.com/inward/record.url?scp=21144466500&partnerID=8YFLogxK

U2 - 10.1007/BF01192443

DO - 10.1007/BF01192443

M3 - Article

AN - SCOPUS:21144466500

SN - 0178-8051

VL - 94

SP - 163

EP - 187

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 2

ER -

A new ideal metric with applications to multivariate stable limit theorems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this