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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A Monte Carlo algorithm for weighted integration over $\mathbb{R} ^d$


Authors: Piotr Gajda, Youming Li, Leszek Plaskota and Grzegorz W. Wasilkowski
Journal: Math. Comp. 73 (2004), 813-825
MSC (2000): Primary 65D30, 65C05
Published electronically: August 19, 2003
MathSciNet review: 2031407
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Abstract | References | Similar Articles | Additional Information

Abstract: We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain $\mathbb{R} ^d$. The algorithm and its desirable theoretical properties are derived based on certain stochastic assumptions about the integrands. It is easy to implement, enjoys $O(n^{-1/2})$ convergence rate, and uses only standard random number generators. Numerical results are also included.


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Additional Information

Piotr Gajda
Affiliation: Department of Mathematics, Informatics, and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Email: piotrg@mimuw.edu.pl

Youming Li
Affiliation: Mathematics and Computer Science Department, Georgia Southern University, 0203 Georgia Avenue, Statesboro, Georgia 30460-8093
Email: yming@gasou.edu

Leszek Plaskota
Affiliation: Department of Mathematics, Informatics, and Mechanics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland
Email: leszekp@mimuw.edu.pl

Grzegorz W. Wasilkowski
Affiliation: Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, Kentucky 40506-0046
Email: greg@cs.uky.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01564-3
PII: S 0025-5718(03)01564-3
Keywords: Numerical multiple integration, Monte Carlo methods, average case error
Received by editor(s): February 18, 2002
Received by editor(s) in revised form: July 23, 2002
Published electronically: August 19, 2003
Article copyright: © Copyright 2003 American Mathematical Society