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

Gajda, Piotr; Li, Youming; Plaskota, Leszek; Wasilkowski, Grzegorz

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

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.

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