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August, 1981 An Invariance Principle for Certain Dependent Sequences
C. M. Newman, A. L. Wright
Ann. Probab. 9(4): 671-675 (August, 1981). DOI: 10.1214/aop/1176994374

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

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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

Information

Published: August, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0465.60009
MathSciNet: MR624694
Digital Object Identifier: 10.1214/aop/1176994374

Subjects:
Primary: 60B10
Secondary: 60F05

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 4 • August, 1981
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