Comparison of Sums of independent Identically Distributed Random Variables

Details Comparison of Sums of independent Identically Distributed Random Variables Comparison of Sums of independent Identically Distributed Random Variables

1993-10-07

arxiv.org/abs/math/9310214v2

Prob. and Math. Stat. 14, (1993), 281-285

Mathematics

Functional Analysis

Scientific paper

Let S_k be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ||S_k|| with that of ||S_j||, and deduce some tail distribution maximal inequalities. Theorem: There is universal constant c such that for j < k Pr(||S_j|| > t) <= c Pr(||S_k|| > t/c).

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