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On Quasi-Monte Carlo Rules Achieving Higher Order Convergence

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Monte Carlo and Quasi-Monte Carlo Methods 2008

Abstract

Quasi-Monte Carlo rules which can achieve arbitrarily high order of convergence have been introduced recently. The construction is based on digital nets and the analysis of the integration error uses Walsh functions. Various approaches have been used to show arbitrarily high convergence. In this paper we explain the ideas behind higher order quasi-Monte Carlo rules by leaving out most of the technical details and focusing on the main ideas.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia

    Josef Dick

Authors
  1. Josef Dick
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Correspondence to Josef Dick .

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Editors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, Montreal, H3C 3J7, Canada

    Pierre L' Ecuyer

  2. Dept. Statistics, Stanford University, Serra Mall 390, Stanford, 94305-4065, U.S.A.

    Art B. Owen

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Dick, J. (2009). On Quasi-Monte Carlo Rules Achieving Higher Order Convergence. In: L' Ecuyer, P., Owen, A. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04107-5_5

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