A strong renewal theorem for generalized renewal functions in the infinite mean case
type: Item
instance of: scholarly article
title: A strong renewal theorem for generalized renewal functions in the infinite mean case
zbMATH Open document ID: 0627.60081
DOI: 10.1007/BF00959611
author: Kevin K. Anderson
author: K. B. Athreya
publication date: 1988-01-01T00:00:00Z
review text: Let F(x) be a nonarithmetic c.d.f. on (0,\(\infty)\) such that \(1- F(x)=x^{-\alpha}L(x)\), where L(x) is slowly varying and \(0\leq \alpha \leq 1\). Let a(x) be regularly varying with exponent \(\beta\) \(\geq -1\). A strong renewal theorem (of Blackwell type) for generalized renewal functions of the form G(t)\(\equiv \sum ^{\infty}_{n=0}a(n)F^ n(t)\) is proved here, thus extending recent work of \textit{P. Embrechts}, \textit{M. Maejima} and \textit{E. Omey} [Ann. Probab. 12, 561-570 (1984; Zbl 0537.60087)] and that of \textit{K. B. Erickson} [Trans. Am. Math. Soc. 151, 263-291 (1970; Zbl 0212.516)].
Mathematics Subject Classification ID: 60K05
zbMATH DE Number: 4020149
zbMATH Keywords: strong renewal theorem
zbMATH Keywords: generalized renewal function
zbMATH Keywords: regular variation
MaRDI profile type: Publication
cites work: A renewal theorem of Blackwell type
cites work: Some Limit Theorems for Generalized Renewal Measures
cites work: On subordinated distributions and random record processes
cites work: Strong Renewal Theorems with Infinite Mean
cites work: Harmonic renewal measures
cites work: On harmonic renewal measures
cites work: Regular variation of the tail of a subordinated probability distribution
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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description: scientific article; zbMATH DE number 4020149