The Annals of Probability

Measuring the magnitude of sums of independent random variables

Paweł Hitczenko and Stephen Montgomery-Smith

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

Article information

Ann. Probab., Volume 29, Number 1 (2001), 447-466.

First available in Project Euclid: 21 December 2001

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G50: Sums of independent random variables; random walks 60E15: Inequalities; stochastic orderings 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 46B09: Probabilistic methods in Banach space theory [See also 60Bxx]

Sum of independent random variables tail distributions decreasing rearrangement pth moment rearrangement invariant space disjoint sum maximal function Hoffmann-Jørgensen/Klass-Nowicki Inequality Lévy Property


Hitczenko, Paweł; Montgomery-Smith, Stephen. Measuring the magnitude of sums of independent random variables. Ann. Probab. 29 (2001), no. 1, 447--466. doi:10.1214/aop/1008956339.

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