Central limit theorem for associated random variables

In this paper, we investigate an functional central limit theorem for a nonstatioaryd-parameter array of associated random variables applying the criterion of the tightness condition in Bickel and Wichura1971]. Our results imply an extension to the nonstatioary case of invariance principle of Burton and Kim(1988) and analogous results for thed-dimensional associated random measure. These results are also applied to show a new functional central limit theorem for Poisson cluster random variables.