A further generalization of the arc-sine law
Chris C. Heyde · Journal of the Australian Mathematical Society · 1968
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.