Affine normability of partial sums of I.I.D. random vectors: A characterization

DOI10.1007/BF00532663zbMath0547.60027MaRDI QIDQ3339023

Michael J. Klass, Marjorie G. Hahn

Publication date: 1985

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

zbMATH Keywords

tightnessgeneralized domain of attractionstochastic compactnessoperator-stable law

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Convergence of probability measures (60B10)

Related Items (11)

On the joint distribution of ladder variables of random walk ⋮ Strong renewal theorems and local large deviations for multivariate random walks and renewals ⋮ Operator stable laws: Series representations and domains of normal attraction ⋮ The structure of generalized domains of semistable attraction ⋮ A bivariate local limit theorem ⋮ Pseudomoments for Generalized Domains of Attraction ⋮ On a multivariate strong renewal theorem ⋮ On the Existence and Convergence of Pseudomoments for Variables in the Domain of Normal Attraction of an Operator Stable Distribution ⋮ Matrix normalized convergence of a Lévy process to normality at zero ⋮ Regular variation and generalized domains of attraction in \(\mathbb{R}^ k\) ⋮ The structure of the exponents and symmetries of an operator stable measure

Cites Work

• Pointwise translation of the Radon transform and the general central limit problem
• Operator-stable distributions and stable marginals
• Matrix normalization of sums of random vectors in the domain of attraction of the multivariate normal
• The multidimensional central limit theorem for arrays normed by affine transformations
• Operator-stable laws
• The domain of normal attraction of an operator-stable law
• On a Uniform Limit Theorem of A. N. Kolmogorov
• Operator-Stable Probability Distributions on Vector Groups
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