## The Annals of Probability

### On the Convergence Rate in the Central Limit Theorem for Associated Processes

Thomas Birkel

#### Abstract

We give uniform rates of convergence in the central limit theorem for associated processes with finite third moment. No stationarity is required. Using a coefficient $u(n)$ which describes the covariance structure of the process, we obtain a convergence rate $O(n^{-1/2}\log^2n)$ if $u(n)$ exponentially decreases to 0. An example shows that such a rate can no longer be obtained if $u(n)$ decreases only as a power.

#### Article information

Source
Ann. Probab., Volume 16, Number 4 (1988), 1685-1698.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991591

Digital Object Identifier
doi:10.1214/aop/1176991591

Mathematical Reviews number (MathSciNet)
MR958210

Zentralblatt MATH identifier
0658.60039

JSTOR