Generation of non-uniform low-discrepancy sequences in the multidimensional case

Natalia Roşca

doi:10.33993/jnaat352-847

Authors

Natalia Roşca “Babes-Bolyai” University, Romania

DOI:

https://doi.org/10.33993/jnaat352-847

Keywords:

discrepancy, uniformly distributed sequences, \(G\)-discrepancy, \(G\)-distributed sequences, low-discrepancy sequences, quasi-Monte Carlo integration, interpolation

Abstract views: 216

Abstract

In this paper we extend the results we obtained in an earlier paper, from the one-dimensional case to the \(s\)-dimensional case. We propose two inversion type methods for generating \(G\)-distributed low-discrepancy sequences in \([0,1]^{s}\), where \(G\) is an arbitrary distribution function. Our methods are based on the approximation of the inverses of the marginal distribution functions using linear Lagrange interpolation or cubic Hermite interpolation. We also determine upper bounds for the \(G\)-discrepancy of the sequences we generate using the proposed methods.

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