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Weak limits for the diaphony

  • Hannes Leeb
Part of the Lecture Notes in Statistics book series (LNS, volume 127)

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.

Keywords

Central Limit Theorem Gaussian Process Weak Convergence Asymptotic Distribution Explicit Representation 
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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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