Abstract
Introduction. These results are generalizations of a theorem of Chung [I ] on the limiting distribution of the number of crossings of a value, c, by the successive partial sums of a sequence of independent random variables, and of theorems by Chung and Erdos [3 ] on the lower limits of such sums. Two of these theorems concern the case of independent, equidistributed random variables whose distributions have an absolutely continuous component (Case A). The others are for binomial variates (Case B). We extend the results of Case A to sums of independent random variables whose distributions need not be the same, and those of Case B to sums of independent and equidistributed random variables of the lattice type. Let {X } be a sequence of independent random variables whose c.d.f.'s, { Fn(x) }, need not be the same. We use the usual notations:
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