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

Paulo Eduardo Oliveira, Charles Suquet (1995)

Commentationes Mathematicae Universitatis Carolinae

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.

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