## The Annals of Probability

### Moment Bounds for Associated Sequences

Thomas Birkel

#### Abstract

Let $\{X_j: j \in \mathbb{N}\}$ be a sequence of associated random variables with zero mean and let $r > 2$. We give two conditions--on the moments and on the covariance structure of the process--which guarantee that $\sup_{m \in \mathbb{N} \cup \{0\}} E| \sum^{m+n}_{j=m+1} X_j|^r = O(n^{r/2})$ holds. Examples show that neither condition can be weakened.

#### Article information

Source
Ann. Probab., Volume 16, Number 3 (1988), 1184-1193.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176991684

Digital Object Identifier
doi:10.1214/aop/1176991684

Mathematical Reviews number (MathSciNet)
MR942762

Zentralblatt MATH identifier
0647.60039

JSTOR