of independent random variables

**Pawe Hitczenko ^{1}
Department of Mathematics and Computer Science
Drexel University
Philadelphia, PA 19104
phitczen@mcs.drexel.edu
http://www.mcs.drexel.edu/~phitczen
Stephen Montgomery-Smith^{2}
Department of Mathematics
University of Missouri-Columbia
Columbia, MO 65211
stephen@math.missouri.edu
http://faculty.missouri.edu/~stephen**

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
th moment, and between the th moment and
the rearrangement invariant norms.

Keywords: sum of independent random variables, tail distributions, decreasing rearrangement, 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.

Keywords: sum of independent random variables, tail distributions, decreasing rearrangement, 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.

- Introduction
- Notation and definitions
- The Klass-Nowicki Inequality
- The Lévy Property
- Tail distributions
- norms
- Rearrangement invariant spaces
- Bibliography
- About this document ...

Stephen Montgomery-Smith 2002-10-30