Probabilistic error bounds for the discrepancy of mixed sequences

Aistleitner Christoph () and Hofer Markus ()
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Aistleitner Christoph: Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria
Hofer Markus: Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria

Monte Carlo Methods and Applications, 2012, vol. 18, issue 2, 181-200

Abstract: In many applications Monte Carlo (MC) sequences or Quasi-Monte Carlo (QMC) sequences are used for numerical integration. In moderate dimensions the QMC method typically yield better results, but its performance significantly falls off in quality if the dimension increases. One class of randomized QMC sequences, which try to combine the advantages of MC and QMC, are so-called mixed sequences, which are constructed by concatenating a d-dimensional QMC sequence and an ()-dimensional MC sequence to obtain a sequence in dimension s. Ökten, Tuffin and Burago proved probabilistic asymptotic bounds for the discrepancy of mixed sequences, which were refined by Gnewuch. In this paper we use an interval partitioning technique to obtain improved probabilistic bounds for the discrepancy of mixed sequences. By comparing them with lower bounds we show that our results are almost optimal.

Keywords: Monte Carlo; Quasi-Monte Carlo; discrepancy; hybrid sequences; mixed sequences; probabilistic methods (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1515/mcma-2012-0006

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