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Measuring the magnitude of sums
of independent random variables

Pawe Hitczenko1
Department of Mathematics and Computer Science
Drexel University
Philadelphia, PA 19104

Stephen Montgomery-Smith2
Department of Mathematics
University of Missouri-Columbia
Columbia, MO 65211


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 Lévy property. We then give a connection between the tail distribution and the $ p$th moment, and between the $ p$th moment and the rearrangement invariant norms.

Keywords: sum of independent random variables, tail distributions, decreasing rearrangement, $ p$th moment, rearrangement invariant space, disjoint sum, maximal function, Hoffmann-Jørgensen/Klass-Nowicki Inequality, Lévy Property.

A.M.S. Classification (1991): Primary 60G50, 60E15, 46E30; Secondary 46B09.

Stephen Montgomery-Smith 2002-10-30