A note on conjugate \(\Pi\)-variation and a weak limit theorem for the number of renewals
type: Item
instance of: scholarly article
title: A note on conjugate \(\Pi\)-variation and a weak limit theorem for the number of renewals
zbMATH Open document ID: 0632.60084
DOI: 10.1016/0167-7152(88)90111-3
author: Kevin K. Anderson
author: K. B. Athreya
published in: Statistics \& Probability Letters
publication date: 1988-01-01T00:00:00Z
review text: Let \(X_ 1,X_ 2,..\). be i.i.d. and positive random variables and put \[ N(t)=\max \{k: X_ 1+...+X_ k\leq t\}. \] If the tails of \(X_ i\) are regularly varying with index -1 then it is known that N(t), suitably normalized, tends in distribution to a stable law of order 1 as \(t\to \infty\). The authors give an alternative expression for the normalizing functions and discuss related conjugation concepts.
reviewed by: Rudolf Grübel
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 26A12
zbMATH DE Number: 4028570
zbMATH Keywords: renewal theory
zbMATH Keywords: regular variation
zbMATH Keywords: conjugation concepts
MaRDI profile type: Publication
full work available at URL: 0167-7152(88)90111-3
OpenAlex ID: W2091186354
cites work: Q3473882
cites work: Limit theorems for regenerative phenomena, recurrent events and renewal theory
cites work: Q3258458
cites work: Fluctuation Theory of Recurrent Events
cites work: Q5512461
cites work: Conjugate \(\pi\)-variation and process inversion
cites work: Regularly varying functions in the theory of simple branching processes
description: scientific article; zbMATH DE number 4028570