More on \(p\)-stable convex sets in Banach spaces
type: Item
instance of: scholarly article
title: More on \(p\)-stable convex sets in Banach spaces
zbMATH Open document ID: 0970.60023
DOI: 10.1023/A:1007726708227
author: Yu. Davydov
author: Alfredas Račkauskas
author: V. Paulauskas
published in: Journal of Theoretical Probability
publication date: 2001-10-16T00:00:00Z
review text: The authors first translate into LePage type series representation, and Poisson integral representation, the representation of \(p\)-stable random compact convex sets of a Banach space of the reviewer and \textit{M. G. Hahn} [Ann. Probab. 13, 447--468 (1985; Zbl 0575.60014)]. Then, they obtain an invariance principle for sums of random sets in the domain of attraction of a \(p\)-stable random set, and specialize the result to the case of random segments, for which they also study singularity questions. Perhaps more interestingly, they propose new estimators of the exponent \(p\) and the spectral measure \(\nu\) of a stable random variable in \(\mathbb R^d\).
Mathematics Subject Classification ID: 60B11
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46N30
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 1428469
zbMATH Keywords: stable convex sets
zbMATH Keywords: stable laws
zbMATH Keywords: parameter estimation
reviewed by: Evarist Giné
MaRDI profile type: Publication
full work available at URL: a:1007726708227
OpenAlex ID: W77193391
description: scientific article; zbMATH DE number 1428469