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Average equidistribution and statistical independence properties of digital inversive pseudorandom numbers over parts of the period
Author(s):
Frank
Emmerich.
Journal:
Math. Comp.
71
(2002),
781-791.
MSC (2000):
Primary 65C10;
Secondary 11K45
Posted:
October 25, 2001
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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
DOI:
10.1090/S0025-5718-01-01328-X
PII:
S 0025-5718(01)01328-X
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
Posted:
October 25, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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