Monte Carlo and Quasi-Monte Carlo Methods 1996

Volume 127 of the series Lecture Notes in Statistics pp 330-339

Weak limits for the diaphony

  • Hannes LeebAffiliated withHannes Leeb Institut für Mathematik, Universität Salzburg

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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.