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Average equidistribution and statistical independence properties of digital inversive pseudorandom numbers over parts of the period

Author: Frank Emmerich
Journal: Math. Comp. 71 (2002), 781-791
MSC (2000): Primary 65C10; Secondary 11K45
Published electronically: October 25, 2001
MathSciNet review: 1885628
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Abstract | References | Similar Articles | Additional Information

Abstract: This article deals with the digital inversive method for generating uniform pseudorandom numbers. Equidistribution and statistical independence properties of the generated pseudorandom number sequences over parts of the period are studied based on the distribution of tuples of successive terms in the sequence. The main result is an upper bound for the average value of the star discrepancy of the corresponding point sets. Additionally, lower bounds for the star discrepancy are established. The method of proof relies on bounds for exponential sums.

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Additional Information

Frank Emmerich
Affiliation: T-Nova Deutsche Telekom Innovationsgesellschaft, Technologiezentrum, Am Kavalleriesand 3, D-64295 Darmstadt, F. R. Germany

Keywords: Uniform pseudorandom numbers, digital inversive method, average equidistribution behaviour, average statistical independence properties, star discrepancy, exponential sums
Received by editor(s): November 10, 1999
Received by editor(s) in revised form: July 12, 2000
Published electronically: October 25, 2001
Article copyright: © Copyright 2001 American Mathematical Society