Quasi-Monte Carlo, Discrepancies and Error Estimates

Details Quasi-Monte Carlo, Discrepancies and Error Estimates Quasi-Monte Carlo, Discrepancies and Error Estimates

1996-11-12

arxiv.org/abs/physics/9611010v1

Physics

Computational Physics

9 pages, standard LaTeX, no special macros. (presented at the 2nd International Conference on Monte Carlo and Quasi-Monte Carl

Scientific paper

We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets, and on the other hand uses information on the degree of uniformity of the point set actually used, in the form of a discrepancy or diaphony. A few examples of such discrepancies are given. We derive the distribution of our error estimate in the limit of large number of points. In many cases, Gaussian central limits are obtained. We also present numerical results for the quadratic star-discrepancy for a number of quasi-random sequences.

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