On coupling of renewal processes with use of failure rates
type: Item
instance of: scholarly article
title: On coupling of renewal processes with use of failure rates
zbMATH Open document ID: 0611.60086
DOI: 10.1016/0304-4149(86)90109-2
author: Torgny Lindvall
published in: Stochastic Processes and their Applications
publication date: 1986-01-01T00:00:00Z
review text: Besides the classical tools for renewal processes coupling methods proved to be successful. Especially asymptotic results for renewal processes are shown by coupling the process to a stationary renewal process, which is easier to handle. \textit{M. Brown} [Ann. Probab. 8, 227-240 (1980; Zbl 0429.60084)] considered monotonicity properties for renewal processes like decreasing (increasing) failure rates of the lifetime distribution. In this paper the author introduces an appropriate coupling for renewal processes and shows, that most of Brown's results can be deduced from coupling methods, for example sharp lower bounds for the renewal function. Additionally he obtains rates of convergence toward stationarity.
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 3988424
zbMATH Keywords: coupling methods
zbMATH Keywords: stationary renewal process
zbMATH Keywords: failure rates of the lifetime distribution
reviewed by: Uwe Rösler
MaRDI profile type: Publication
full work available at URL: 0304-4149(86)90109-2
OpenAlex ID: W1991232485
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description: scientific article; zbMATH DE number 3988424