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April, 1978 Limit Theorems for Multiply Indexed Mixing Random Variables, with Application to Gibbs Random Fields
Carla C. Neaderhouser
Ann. Probab. 6(2): 207-215 (April, 1978). DOI: 10.1214/aop/1176995568

Abstract

If $d$ is a fixed positive integer, let $\Lambda_N$ be a finite subset of $Z^d$, the lattice points of $\mathbb{R}^d$, with $\Lambda_N \uparrow Z^d$ and satisfying certain regularity properties. Let $(X_{N, Z})_{Z\in\Lambda_N}$ be a collection of random variables which satisfy a mixing condition and whose partial sums $X_N = \sum_{Z\in\Lambda_N} X_{N, Z}$ have uniformly bounded variances. Limit theorems, including a central limit theorem, are obtained for the sequence $X_N$. The results are applied to Gibbs random fields known to satisfy a sufficiently strong mixing condition.

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Carla C. Neaderhouser. "Limit Theorems for Multiply Indexed Mixing Random Variables, with Application to Gibbs Random Fields." Ann. Probab. 6 (2) 207 - 215, April, 1978. https://doi.org/10.1214/aop/1176995568

Information

Published: April, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0374.60033
MathSciNet: MR482951
Digital Object Identifier: 10.1214/aop/1176995568

Subjects:
Primary: 60F05
Secondary: 60F15

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 2 • April, 1978
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