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A note on sums of independent random variables

Paweł Hitczenko·Stephen Montgomery-Smith
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Abstract

In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Latała on bounds on moments of such sums. We also give a new proof of Latała's result for nonnegative random variables, and improve one of the constants in his inequality.

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Paweł Hitczenko, Stephen Montgomery-Smith. 1999-12-03. A note on sums of independent random variables. https://arxiv.org/abs/math/9804068

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