On the Discrepancy of Random Walks on the Circle
Keyword(s):
AbstractLet X1,X2,... be i.i.d. absolutely continuous random variables, let {S_k} = \sum\nolimits_{j = 1}^k {{X_j}} (mod 1) and let D*N denote the star discrepancy of the sequence (Sk)1≤k≤N. We determine the limit distribution of \sqrt N D_N^* and the weak limit of the sequence \sqrt N \left( {{F_N}(t) - t} \right) in the Skorohod space D[0, 1], where FN (t) denotes the empirical distribution function of the sequence (Sk)1≤k≤N.
1977 ◽
Vol 41
(2)
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pp. 115-137
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1971 ◽
Vol 8
(02)
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pp. 321-330
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1965 ◽
Vol 8
(1)
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pp. 93-103
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1967 ◽
Vol 19
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pp. 550-558
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1994 ◽
Vol 20
(1)
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pp. 81-84
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