Dynamical system generated by algebraic method and low discrepancy sequences

Mori Makoto and Mori Masaki
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Mori Makoto: Department of Mathematics, College of Humanities and Sciences, Nihon University, Japan
Mori Masaki: Department of Mathematics, University of Tokyo, Japan

Monte Carlo Methods and Applications, 2012, vol. 18, issue 4, 327-351

Abstract: For higher dimensional cases, the essential spectrum radius of the Perron–Frobenius operator is usually greater than (the definition is given below) even if we restrict its domain to a suitable space. In this article, using algebraic method, we construct a transformation whose essential spectrum radius equals . By this transformation, we can construct low discrepancy sequences.

Keywords: Perron–Frobenius operator; van der Corput sequence (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1515/mcma-2012-0012

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