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Mathematics of Computation

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Quasi-Monte Carlo integration over $\mathbb{R}^d$

Authors: Peter Mathé and Gang Wei
Journal: Math. Comp. 73 (2004), 827-841
MSC (2000): Primary 65C05; Secondary 68Q25
Published electronically: August 7, 2003
MathSciNet review: 2031408
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Abstract: In this paper we show that a wide class of integrals over $\mathbb R^d$ with a probability weight function can be evaluated using a quasi-Monte Carlo algorithm based on a proper decomposition of the domain $\mathbb R^d$ and arranging low discrepancy points over a series of hierarchical hypercubes. For certain classes of power/exponential decaying weights the algorithm is of optimal order.

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Additional Information

Peter Mathé
Affiliation: Weierstraß Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D-10117 Berlin, Germany

Gang Wei
Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon, Hong Kong

Keywords: Quasi--Monte Carlo integration, elliptically contoured distributions
Received by editor(s): June 11, 2002
Received by editor(s) in revised form: October 10, 2002
Published electronically: August 7, 2003
Article copyright: © Copyright 2003 American Mathematical Society