The Annals of Probability

Limit Theorems for Multiply Indexed Mixing Random Variables, with Application to Gibbs Random Fields

Carla C. Neaderhouser

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 6, Number 2 (1978), 207-215.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995568

Digital Object Identifier
doi:10.1214/aop/1176995568

Mathematical Reviews number (MathSciNet)
MR482951

Zentralblatt MATH identifier
0374.60033

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F15: Strong theorems

Keywords
Weakly dependent random variables mixing random variables central limit problem random fields

Citation

Neaderhouser, Carla C. Limit Theorems for Multiply Indexed Mixing Random Variables, with Application to Gibbs Random Fields. Ann. Probab. 6 (1978), no. 2, 207--215. doi:10.1214/aop/1176995568. https://projecteuclid.org/euclid.aop/1176995568


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