Constructing a new class of low-discrepancy sequences by using the β-adic transformation

Syoiti Ninomiya

Mathematics and Computers in Simulation (MATCOM), 1998, vol. 47, issue 2, 403-418

Abstract: It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods [5]. In this paper, a new class of low-discrepancy sequences Nβ is constructed by using the ergodic theoretical transformation which is called β-adic transformation [7, 8]. Here, β is a real number greater than 1. When β is an integer greater than 2, Nβ becomes the classical van der Corput sequence in base β. Therefore, the class Nβ can be regarded as a generalization of the van der Corput sequence. It is shown that for some special β, the discrepancy of this sequence decreases in the fastest order O(N−1logN). We give the numerical results of discrepancy of Nβ for some βs. Pagès [6] also generalized van der Corput sequence in a different direction by using an ergodic transformation.

Keywords: Discrepancy; Ergodic theory; Low-discrepancy sequence; Numerical integration; Quasi Monte Carlo method (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:47:y:1998:i:2:p:403-418

DOI: 10.1016/S0378-4754(98)00115-3

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