On the asymptotic behavior of the harmonic renewal measure
type: Item
instance of: scholarly article
title: On the asymptotic behavior of the harmonic renewal measure
zbMATH Open document ID: 0917.60090
DOI: 10.1023/A:1022627704800
published in: Journal of Theoretical Probability
publication date: 1999-08-02T00:00:00Z
review text: Let \(X_1,X_2,\dots\) be independent random variables with distribution function \(F\) and negative mean, let \(S_0=0\), \(S_n=\sum^n_{k=1}X_k\) be the associated partial sums. Then the harmonic renewal measure \(U\) is given by \(U(A)= \sum^\infty_{n=1} n^{-1}P (S_n\in A)\). The main result of the paper deals with the connection between the behaviour of \(x\to 1-F(x)\) and \(x\to U([x,\infty))\) as \(x\to\infty\).
reviewed by: Rudolf Grübel
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 1208789
zbMATH Keywords: tail behaviour
zbMATH Keywords: random walk
zbMATH Keywords: subexponential distributions
zbMATH Keywords: Banach algebras
author: M. S. Sgibnev
MaRDI profile type: Publication
full work available at URL: a:1022627704800
OpenAlex ID: W48320499
description: scientific article; zbMATH DE number 1208789