Displaying similar documents to “An L 2 [ 0 , 1 ] invariance principle for LPQD random variables.”

Convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables

Yongfeng Wu, Dingcheng Wang (2012)

Applications of Mathematics

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In this paper the authors study the convergence properties for arrays of rowwise pairwise negatively quadrant dependent random variables. The results extend and improve the corresponding theorems of T. C. Hu, R. L. Taylor: On the strong law for arrays and for the bootstrap mean and variance, Int. J. Math. Math. Sci 20 (1997), 375–382.

An invariance principle in L 2 [ 0 , 1 ] for non stationary ϕ -mixing sequences

Paulo Eduardo Oliveira, Charles Suquet (1995)

Commentationes Mathematicae Universitatis Carolinae

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Invariance principle in L 2 ( 0 , 1 ) is studied using signed random measures. This approach to the problem uses an explicit isometry between L 2 ( 0 , 1 ) and a reproducing kernel Hilbert space giving a very convenient setting for the study of compactness and convergence of the sequence of Donsker functions. As an application, we prove a L 2 ( 0 , 1 ) version of the invariance principle in the case of ϕ -mixing random variables. Our result is not available in the D ( 0 , 1 ) -setting.