The Asymptotic Behavior of the Average $L^p-$Discrepancies and a Randomized Discrepancy
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This paper gives the limit of the average $L^p-$star and the average $L^p-$extreme discrepancy for $[0,1]^d$ and $0 < p < \infty$. This complements earlier results by Heinrich, Novak, Wasilkowski & Woźnia-kowski, Hinrichs & Novak and Gnewuch and proves that the hitherto best known upper bounds are optimal up to constants.We furthermore introduce a new discrepancy $D_{N}^{\mathbb{P}}$ by taking a probabilistic approach towards the extreme discrepancy $D_{N}$. We show that it can be interpreted as a centralized $L^1-$discrepancy $D_{N}^{(1)}$, provide upper and lower bounds and prove a limit theorem.
1996 ◽
Vol 28
(04)
◽
pp. 965-981
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1999 ◽
Vol 36
(01)
◽
pp. 105-118
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Keyword(s):
1996 ◽
Vol 28
(4)
◽
pp. 965-981
◽
1996 ◽
Vol 118
(3)
◽
pp. 434-438
◽
1967 ◽
Vol 9
(2)
◽
pp. 149-156
◽
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