Open Access
Translator Disclaimer
January 2000 The limit points in $\bar{R^d}$ of averages of i.i.d. random variables
K. Bruce Erickson
Ann. Probab. 28(1): 498-510 (January 2000). DOI: 10.1214/aop/1019160128

Abstract

Given any closed subset $C$ of $\bar{R^d}$, containing a pair of antipodal points at $\infty$, there is a sequence of independent and identically distributed random variables $\mathbf{X}_i}$ such that the set of limit points (in the topology of $\bar{R^d}$ of $\{(\mathbf{X}_1 + \cdots + \mathbf{X}_t)/t\}_{t \geq 1}$ equals $C$. Here $\bar{R^d}$ is the compact space gotten by “adjoining the sphere, $S^{d -1}\infty$ at infinity.”

Citation

Download Citation

K. Bruce Erickson. "The limit points in $\bar{R^d}$ of averages of i.i.d. random variables." Ann. Probab. 28 (1) 498 - 510, January 2000. https://doi.org/10.1214/aop/1019160128

Information

Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1130.60305
MathSciNet: MR1756014
Digital Object Identifier: 10.1214/aop/1019160128

Subjects:
Primary: 60F05, 60F15

Rights: Copyright © 2000 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.28 • No. 1 • January 2000
Back to Top