1996/11/12 by F. James, James, Fred, Jiri Hoogland +3
Mathematics · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.physics/9611010
openalex publication_date 1996/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.