The Annals of Probability

A Two-Parameter Maximal Ergodic Theorem with Dependence

Terry R. McConnell

Full-text: Open access

Abstract

Let $X_1, X_2, \ldots$ and $Y_1, Y_2, \ldots$ be independent sequences of i.i.d. $U(0, 1)$ random variables. We characterize completely those Borel functions $F$ on $\lbrack 0, 1\rbrack^2$ for which the strong law of large numbers and the maximal ergodic theorem hold for the doubly indexed family $(1/nm)\sum_{i \leq n, j \leq m}F(X_i, Y_j)$.

Article information

Source
Ann. Probab., Volume 15, Number 4 (1987), 1569-1585.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991994

Digital Object Identifier
doi:10.1214/aop/1176991994

Mathematical Reviews number (MathSciNet)
MR905349

Zentralblatt MATH identifier
0656.28011

JSTOR
links.jstor.org

Subjects
Primary: 28D05: Measure-preserving transformations
Secondary: 60G60: Random fields

Keywords
Maximal ergodic theorem strong law of large numbers two-parameter martingales decoupling

Citation

McConnell, Terry R. A Two-Parameter Maximal Ergodic Theorem with Dependence. Ann. Probab. 15 (1987), no. 4, 1569--1585. doi:10.1214/aop/1176991994. https://projecteuclid.org/euclid.aop/1176991994


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