zbMATH — the first resource for mathematics

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.

60F17 Functional limit theorems; invariance principles
Full Text: DOI