A Monte Carlo algorithm for weighted integration over $\mathbb {R}^d$
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- by Piotr Gajda, Youming Li, Leszek Plaskota and Grzegorz W. Wasilkowski PDF
- Math. Comp. 73 (2004), 813-825 Request permission
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.References
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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
- MR Author ID: 189251
- ORCID: 0000-0003-4727-7368
- Email: greg@cs.uky.edu
- Received by editor(s): February 18, 2002
- Received by editor(s) in revised form: July 23, 2002
- Published electronically: August 19, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 813-825
- MSC (2000): Primary 65D30, 65C05
- DOI: https://doi.org/10.1090/S0025-5718-03-01564-3
- MathSciNet review: 2031407