Discrepancy of van der Corput sequences generated by piecewise linear transformations

Ichikawa Yuko and Mori Makoto
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Ichikawa Yuko: 1. Dept. Math. College of Humanities and Sciences, Nihon University 3-25-40 Sakura Jyosui, Setagaya-ku, Tokyo, 156-8550
Mori Makoto: 2. Dept. Natural Sciences, Tokyo National College of Technology, 1220-2 Kunugida-machi, Hachioji-shi, Tokyo, 193-0097

Monte Carlo Methods and Applications, 2004, vol. 10, issue 2, 107-116

Abstract: 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.

Date: 2004
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DOI: 10.1515/156939604777303217

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