A Monte Carlo algorithm for weighted integration over ℝ d

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)813-825
Number of pages13
JournalMathematics of Computation
Issue number246
StatePublished - Apr 2004


  • Average case error
  • Monte Carlo methods
  • Numerical multiple integration

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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