Abstract
Let $X_1, X_2, \cdots$ be a strictly stationary second order sequence which is "associated"; i.e., is such that any two coordinatewise nondecreasing functions of the $X_i$'s (of finite variance) are nonnegatively correlated. If $\sum_j \operatorname{Cov}(X_1, X_j) < \infty$, then the partial sum processes, $W_n(t)$, defined in the usual way so that $W_n(m/n) = (X_1 + \cdots + X_m - mE(X_1))/\sqrt n$ for $m = 1, 2, \cdots$, converge in distribution on $C\lbrack 0, T\rbrack$ to a Wiener process. This result is based on two general theorems concerning associated random variables which are of independent interest.
Citation
C. M. Newman. A. L. Wright. "An Invariance Principle for Certain Dependent Sequences." Ann. Probab. 9 (4) 671 - 675, August, 1981. https://doi.org/10.1214/aop/1176994374
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