Comparison of Sums of independent Identically Distributed Random Variables
Stephen J. Montgomery-Smith
Abstract
Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ||Sk|| with that of ||Sj||, and deduce some tail distribution maximal inequalities. Theorem: There is universal constant c such that for j < k Pr(||Sj|| > t) <= c Pr(||Sk|| > t/c).
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