L p -discrepancy and statistical independence of sequences

Peter J. Grabner; Oto Strauch; Robert Franz Tichy

Czechoslovak Mathematical Journal (1999)

  • Volume: 49, Issue: 1, page 97-110
  • ISSN: 0011-4642

Abstract

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We characterize statistical independence of sequences by the L p -discrepancy and the Wiener L p -discrepancy. Furthermore, we find asymptotic information on the distribution of the L 2 -discrepancy of sequences.

How to cite

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Grabner, Peter J., Strauch, Oto, and Tichy, Robert Franz. "$L^p$-discrepancy and statistical independence of sequences." Czechoslovak Mathematical Journal 49.1 (1999): 97-110. <http://eudml.org/doc/30468>.

@article{Grabner1999,
abstract = {We characterize statistical independence of sequences by the $L^p$-discrepancy and the Wiener $L^p$-discrepancy. Furthermore, we find asymptotic information on the distribution of the $L^2$-discrepancy of sequences.},
author = {Grabner, Peter J., Strauch, Oto, Tichy, Robert Franz},
journal = {Czechoslovak Mathematical Journal},
keywords = {sequences; statistical independence; discrepancy; distribution functions; sequences; statistical independence; discrepancy; distribution functions},
language = {eng},
number = {1},
pages = {97-110},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$L^p$-discrepancy and statistical independence of sequences},
url = {http://eudml.org/doc/30468},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Grabner, Peter J.
AU - Strauch, Oto
AU - Tichy, Robert Franz
TI - $L^p$-discrepancy and statistical independence of sequences
JO - Czechoslovak Mathematical Journal
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 1
SP - 97
EP - 110
AB - We characterize statistical independence of sequences by the $L^p$-discrepancy and the Wiener $L^p$-discrepancy. Furthermore, we find asymptotic information on the distribution of the $L^2$-discrepancy of sequences.
LA - eng
KW - sequences; statistical independence; discrepancy; distribution functions; sequences; statistical independence; discrepancy; distribution functions
UR - http://eudml.org/doc/30468
ER -

References

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  14. On the set of all distribution functions of a sequence, Proceedings of the conference on analytic and elementary number theory: a satellite conference of the European Congress on Mathematics ’96, Vienna, July 18–20, 1996. Dedicated to the honour of the 80th birthday of E. Hlawka, W. G. Nowak et al. (eds.), Universität Wien, 1996, pp. 214–229. (1996) 
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