A Monte Carlo algorithm for weighted integration over ℝ d

Piotr Gajda; Youming Li; Leszek Plaskota; Grzegorz W. Wasilkowski

doi:10.1090/S0025-5718-03-01564-3

A Monte Carlo algorithm for weighted integration over ℝ ^d

Piotr Gajda, Youming Li, Leszek Plaskota, Grzegorz W. Wasilkowski

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain 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.

Original language	English
Pages (from-to)	813-825
Number of pages	13
Journal	Mathematics of Computation
Volume	73
Issue number	246
DOIs	https://doi.org/10.1090/S0025-5718-03-01564-3
State	Published - Apr 2004

Keywords

Average case error
Monte Carlo methods
Numerical multiple integration

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

Access to Document

10.1090/S0025-5718-03-01564-3

Cite this

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abstract = "We present and analyze a new randomized algorithm for numerical computation of weighted integrals over the unbounded domain 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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