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A functional central limit theorem for positively dependent random variables. (English) Zbl 0770.60037
A pair of random variables, $$X$$ and $$Y$$, is positive quadrant dependent if for every real $$x$$ and $$y$$, $$P[X>x,Y>y]$$ is greater than or equal to $$P[X>x]P[Y>y]$$. A sequence of random variables is linearly positive quadrant dependent if every pair of linear combinations of these variables over disjoint sets of indices is positive quadrant dependent. This paper establishes a functional central limit theorem for nonstationary sequences of linearly positive dependent variables under moment conditions and conditions on the rate of decrease of certain covariance expressions.

##### MSC:
 60F17 Functional limit theorems; invariance principles
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