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A further generalization of the arc-sine law
Published online by Cambridge University Press: 09 April 2009
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Let Xi, i = 1,2,3,… be a sequence of independent and identically distributed random variables and write S0 = 0, Sn = ∑ni=1Xi, n ≧ 1. Let In(0), In(1), …, In (n) be that unique permutaion of 1, 2, …, n such that SIn(0) ≦ SIn(1) ≦ … ≦ SIn(n) and such that if Si = Sk with i < k then In(k) < In(j). Thus, In(j) is an index of the j-th largest partial sum.
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- Copyright © Australian Mathematical Society 1968
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