Quasi-Monte Carlo algorithms for unbounded, weighted integration problems

被引：15

作者：

Hartinger, E ^{[1
]}

Kainhofer, RF ^{[1
]}

Tichy, RF ^{[1
]}

机构：

[1] Graz Univ Technol, Dept Math, A-8010 Graz, Austria

来源：

JOURNAL OF COMPLEXITY | 2004年 / 20卷 / 05期

基金：

奥地利科学基金会;

关键词：

quasi-Monte Carlo integration; weighted integration; non-uniformly distributed low-discrepancy sequences;

D O I：

10.1016/j.jco.2003.11.006

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this article we investigate quasi-Monte Carlo (QMC) methods for multidimensional improper integrals with respect to a measure other than the uniform distribution. Additionally, the integrand is allowed to be unbounded at the lower boundary of the integration domain. We establish convergence of the QMC estimator to the value of the improper integral under conditions involving both the integrand and the sequence used. Furthermore, we suggest a modification of an approach proposed by Hlawka and Muck for the creation of low-discrepancy sequences with regard to a given density, which are suited for singular integrands. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：654 / 668

页数：15

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