Weak limits for the diaphony

  • Hannes Leeb
Conference paper

DOI: 10.1007/978-1-4612-1690-2_23

Part of the Lecture Notes in Statistics book series (LNS, volume 127)
Cite this paper as:
Leeb H. (1998) Weak limits for the diaphony. In: Niederreiter H., Hellekalek P., Larcher G., Zinterhof P. (eds) Monte Carlo and Quasi-Monte Carlo Methods 1996. Lecture Notes in Statistics, vol 127. Springer, New York, NY

Abstract

In one dimension, we represent the diaphony as the L2-norm of a random process which is found to converge weakly to a second order stationary Gaussian; up to scaling, this implies the asymptotic distributions of the diaphony and the *-discrepancy to coincide. Further, we show that properly normalized, the diaphony of n points in dimension d is asymptotically Gaussian if both n and d increase with a certain rate.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Hannes Leeb
    • 1
  1. 1.Hannes Leeb Institut für MathematikUniversität SalzburgSalzburgAustria

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