LP-discrepancy and statistical independence of sequences

Czechoslovak Mathematical Journal

Volumn 49, Issue 1, 1999, Pages 97-110

  Grabner, Peter J ^a   Strauch, Oto ^b   Tichy, Robert F ^a  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Discrepancy; Distribution functions; Sequences; Statistical independence

Indexed keywords

EID: 0034354306     PISSN: 00114642     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022460225387     Document Type: Article

References (16)

1. Cameron, R. H., Martin, W. T.: Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations. Bull. Amer. Math. Soc. 51 (1945), 73-90.
2. Doetsch, G.: Handbuch über die Laplace Transformation, II. Birkhäuser Verlag, Basel, 1955.
3. Donsker, M.D.: Justification and extension of Doob's heuristic approach to the Kolmogorov-Smirnov theorems. Ann. Math. Stat. 23 (1952), 277-281.
4. Doob, J.L.: Heuristic approach to the Kolmogorov-Smirnov theorems. Ann. Math. Stat. 20 (1949), 393-403.
5. Grabner, P. J., Tichy, R. F.: Remarks on statistical independence of sequences. Math. Slovaca 44 (1994), 91-94.
6. Grabner, P. J., Strauch, O., Tichy, R. F.: Maldistribution in higher dimensions. Mathematica Pannonica 8 (1997), 215-223.
7. Kac, M.: Probability and related topics in physical sciences. Lectures in Applied Math., Proceedings of a Summer Seminar in Boulder, Col. 1957, Interscience Publishers, London, New York, 1959.
8. Kolmogoroff, A.: Sulla determinazione empirica di una legge di distribuzione. Giorn. Ist. Ital. Attuari 4 (1933), 83-91.
9. Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. John Wiley & Sons, New York, 1974.
10. Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics. Springer, Berlin, Heidelberg, New York, 1966.
11. Rauzy, G.: Propriétés statistiques de suites arithmétiques. Le Mathématicien, No. 15, Collection SUP. Presses Universitaires de France, Paris, 1976.
12. Ray, D.: On spectra of second-order differential operators. Trans. Amer. Math. Soc. 77 (1954), 299-321.
13. 2 discrepancy. Math. Slovaca 44 (1994), 601-632.
14. Strauch, O.: 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.
15. Titchmarsh, E.C.: Eigenfunction Expansions Associated with Second-Order Differential Equations. Oxford University Press, 1946.
16. Winkler, R.: On the distribution behaviour of sequences. Math. Nachrichten 186 (1997), 303-312. To appear.