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January, 1986 On Strong Invariance Principles Under Dependence Assumptions
Ernst Eberlein
Ann. Probab. 14(1): 260-270 (January, 1986). DOI: 10.1214/aop/1176992626


Strong invariance principles with other of approximation $O(t^{1/2-\kappa})$ are obtained for sequences of dependent random variables. The basic dependence assumptions include various generalizations of martingales such as asymptotic martingales (amarts), semiamarts, and mixingales as well as processes characterized by a condition on the Doleans measure. Provided the partial sum process is uniformly integrable, also martingales in the limit and games fairer with time are included. Sufficient conditions for linear growth of the covariance function of the partial sums are given.


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Ernst Eberlein. "On Strong Invariance Principles Under Dependence Assumptions." Ann. Probab. 14 (1) 260 - 270, January, 1986.


Published: January, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0589.60031
MathSciNet: MR815969
Digital Object Identifier: 10.1214/aop/1176992626

Primary: 60F17
Secondary: 60F05 , 60F15 , 60G48

Keywords: Amart , covariance function , Doleans measure , game fairer with time , martingale generalization , martingale in the limit , semiamart , Strong invariance principle

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 1 • January, 1986
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