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September 2016 Marcinkiewicz law of large numbers for outer products of heavy-tailed, long-range dependent data
Hui He
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Adv. in Appl. Probab. 48(3): 672-690 (September 2016).

Abstract

Given a supercritical Galton‒Watson process {Zn} and a positive sequence {εn}, we study the limiting behaviors of ℙ(SZn/Zn≥εn) with sums Sn of independent and identically distributed random variables Xi and m=𝔼[Z1]. We assume that we are in the Schröder case with 𝔼Z1 log Z1<∞ and X1 is in the domain of attraction of an α-stable law with 0<α<2. As a by-product, when Z1 is subexponentially distributed, we further obtain the convergence rate of Zn+1/Zn to m as n→∞.

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Hui He. "Marcinkiewicz law of large numbers for outer products of heavy-tailed, long-range dependent data." Adv. in Appl. Probab. 48 (3) 672 - 690, September 2016.

Information

Published: September 2016
First available in Project Euclid: 19 September 2016

MathSciNet: MR3511765

Subjects:
Primary: 60J80
Secondary: 60F10

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 3 • September 2016
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