Please use this identifier to cite or link to this item: https://doi.org/10.1080/00949650215727
Title: Error analysis of some integration procedures for renewal equation and convolution integrals
Authors: Xie, M. 
Preuss, W.
Cui, L.-R. 
Keywords: Convolution
Error analysis
Numerical methods
Renewal function
Riemann-Stieltjes integral
Issue Date: 1-Jan-2003
Source: Xie, M.,Preuss, W.,Cui, L.-R. (2003-01-01). Error analysis of some integration procedures for renewal equation and convolution integrals. Journal of Statistical Computation and Simulation 73 (1) : 59-70. ScholarBank@NUS Repository. https://doi.org/10.1080/00949650215727
Abstract: When computing convolution integrals such as needed in solving renewal-type integral equations, direct integration of the Riemann-Stieltjes integral can be used. This method has been shown to be simple and accurate with good convergence property. In this paper bounds on the error terms are derived for some direct Riemann-Stieltjes integration methods. The bounds are rough but they are given under very weak assumptions. The bounds are further improved when certain derivability conditions are satisfied. It is shown that, under some continuity assumptions, the convergence is of order 2 as for the case of traditional Riemann integral. This provides the theoretical foundation to the direct Riemann-Stieltjes integration which can be used to approximate Riemann-Stieltjes integrals and in solving renewal-type equations.
Source Title: Journal of Statistical Computation and Simulation
URI: http://scholarbank.nus.edu.sg/handle/10635/63122
ISSN: 00949655
DOI: 10.1080/00949650215727
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

10
checked on Dec 13, 2017

WEB OF SCIENCETM
Citations

9
checked on Oct 27, 2017

Page view(s)

42
checked on Dec 16, 2017

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.