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February, 1984 A Strong Law of Large Numbers for Partial-Sum Processes Indexed by Sets
Richard F. Bass, Ronald Pyke
Ann. Probab. 12(1): 268-271 (February, 1984). DOI: 10.1214/aop/1176993390

Abstract

Let $J = \{1, 2, \cdots\}^d$ and let $\{X_j, \mathbf{j} \in J\}$ be iid with finite mean. Let $S(nA)$ be the sum of those $X_j$'s for which $\mathbf{j}/n \in A$. It is proved in this paper that $S(\cdot)$ satisfies a strong law of large numbers that is uniform over $A \in \mathscr{A}$, where $\mathscr{A}$ is a family of subsets of $\lbrack 0, 1\rbrack^d$ satisfying a mild condition.

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Richard F. Bass. Ronald Pyke. "A Strong Law of Large Numbers for Partial-Sum Processes Indexed by Sets." Ann. Probab. 12 (1) 268 - 271, February, 1984. https://doi.org/10.1214/aop/1176993390

Information

Published: February, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0543.60036
MathSciNet: MR723746
Digital Object Identifier: 10.1214/aop/1176993390

Subjects:
Primary: 60F15
Secondary: 60G99

Keywords: partial-sum processes , processes indexed by sets , Strong law of large numbers

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February, 1984
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