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Measuring the magnitude of sums of independent random variables

Pawel Hitczenko·Stephen Montgomery-Smith
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Abstract

This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Levy property. We then give a connection between the tail distribution and the pth moment, and between the pth moment and the rearrangement invariant norms.

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Pawel Hitczenko, Stephen Montgomery-Smith. 1999-09-09. Measuring the magnitude of sums of independent random variables. https://arxiv.org/abs/math/9909054

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