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.
Citation
Thomas Birkel. "Moment Bounds for Associated Sequences." Ann. Probab. 16 (3) 1184 - 1193, July, 1988. https://doi.org/10.1214/aop/1176991684
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