Semi-attraction domains of semistable laws on topological vector spaces
type: Item
instance of: scholarly article
title: Semi-attraction domains of semistable laws on topological vector spaces
zbMATH Open document ID: 0678.60003
author: Ho Dang Phuc
published in: Acta Mathematica Vietnamica
publication date: 1987-01-01T00:00:00Z
review text: Let E be a locally convex topological vector space. Moreover let p and q be Radon measures on E such that q is convexly tight; and let p belong to the domain of partial attraction of q with respect to a strictly increasing sequence \((n_ k)_{k\geq 1}\) of integers. The main part of this paper is dedicated to the following two theorems: 1. If the sequence \((n_ k/n_{k+1})_{k\geq 1}\) admits an accumulation point in (0,1) then q is semistable. 2. If lim inf \(n_ k/n_{k+1}\) is positive and if q is r-semistable (resp. stable) then p belongs to the domain of r-semi-attraction (resp. to the domain of attraction) of q. These results permit less restrictive definitions of ``semistability'' and of ``domain of semi-attraction''. The proofs are based on a paper by \textit{D. M. Chung}, \textit{B. S. Rajput} and \textit{A. Tortrat} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 60, 209-218 (1982; Zbl 0468.60006)].
Mathematics Subject Classification ID: 60B11
zbMATH DE Number: 4111666
zbMATH Keywords: domain of semi-attraction
zbMATH Keywords: locally convex topological vector space
zbMATH Keywords: Radon measures
zbMATH Keywords: domain of partial attraction
reviewed by: Eberhard Siebert
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4111666