Probabilistic error bounds for the discrepancy of mixed sequences
-
Christoph Aistleitner
und
Markus Hofer
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.
© 2012 by Walter de Gruyter Berlin Boston
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Artikel in diesem Heft
- Masthead
- On the population median estimation using robust extreme ranked set sampling
- A mathematical formalization of the parallel replica dynamics
- A restarted estimation of distribution algorithm for solving sudoku puzzles
- Parallel random number generators in Monte Carlo derivative pricing: An application-based test
- Probabilistic error bounds for the discrepancy of mixed sequences
