Almost certain behavior of row sums of double arrays
The almost certain (probability one) behavior of row sums Open image in new window of double arrays of rowwise independent random variables Xn, i is investigated primarily when the Xn, i assume only the values zero and one. If knpn, the expected number of successes, grows more rapidly than C log n, then Open image in new window converges almost certainly to one. However, when the expected number of successes grows less rapidly than C log n, it no longer determines the asymptotic behavior of Open image in new window and the outcome depends upon additional stochastic assumptions. Two alternative sets of stochastic constraints are imposed and the behavior of Open image in new window under each is analyzed and contrasted. Finally, the case of exponential random variables is considered briefly.
KeywordsTriangular Array Independent Column Poisson Probability Standard Normal Density Poisson Case
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