Error bounds for Quasi-Monte Carlo integration with uniform point sets

Authors:
Harald Niederreiter
Affiliations:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore
Venue:
Journal of Computational and Applied Mathematics
Year:
2003

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Abstract

We establish new error bounds for quasi-Monte Carlo integration for node sets with a special kind of uniformity property. The methods of proving these error bounds work for arbitrary probability spaces. Only the bounds in terms of the modulus of continuity of the integrand require also the structure of a metric space.