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Monte Carlo Methods and Applications

Managing Editor: Sabelfeld, Karl K.

Editorial Board: Binder, Kurt / Bouleau, Nicolas / Chorin, Alexandre J. / Dimov, Ivan / Dubus, Alain / Egorov, Alexander D. / Ermakov, Sergei M. / Halton, John H. / Heinrich, Stefan / Kalos, Malvin H. / Lepingle, D. / Makarov, Roman / Mascagni, Michael / Mathe, Peter / Niederreiter, Harald / Platen, Eckhard / Sawford, Brian R. / Schmid, Wolfgang Ch. / Schoenmakers, John / Simonov, Nikolai A. / Sobol, Ilya M. / Spanier, Jerry / Talay, Denis

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Volume 10, Issue 2

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Discrepancy of van der Corput sequences generated by piecewise linear transformations

Yuko Ichikawa
  • 1. Dept. Math. College of Humanities and Sciences, Nihon University 3-25-40 Sakura Jyosui, Setagaya-ku, Tokyo, 156-8550
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/ Makoto Mori
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  • 2. Dept. Natural Sciences, Tokyo National College of Technology, 1220-2 Kunugida-machi, Hachioji-shi, Tokyo, 193-0097
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Discrepancy of van der Corput sequences constructed by piecewise linear transformations with same slope β > 1 is discussed. If there is no eigenvalues of the Perron-Frobenius operator associated with the dynamical system in |z| > 1/β except 1, the discrepancy equals (logN)k+1/N, where k is the number of the non-Markov endpoints.

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Published in Print: 2004-06-01


Citation Information: Monte Carlo Methods and Applications mcma, Volume 10, Issue 2, Pages 107–116, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/156939604777303217.

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Makoto Mori
Monte Carlo Methods and Applications, 2005, Volume 11, Number 2

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