Moment bounds for associated sequences (Q1104631)

A finite family \(\{X_ 1,...,X_ m\}\) of random variables is said to be associated if for any two coordinatewise nondecreasing functions f and g, \[ Cov(f(X_ 1,...,X_ m),g(X_ 1,...,X_ m))\geq 0. \] An infinite family is associated if every finite subfamily is associated. Let \(\{X_ j\}\) be a sequence of mean zero associated random variables. The author gives two conditions on the moments and convariance structure of the process which guarantee that for \(r>2\), \[ \sup \epsilon | \sum^{m+n}_{j=m+1}X_ j|^ r=O(n^{r}) \] holds. Examples show that the conditions can not be weakened.