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

Paulo Eduardo OliveiraCharles 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.

Mean quadratic convergence of signed random measures

Pierre JacobPaulo Eduardo Oliveira — 1991

Commentationes Mathematicae Universitatis Carolinae

We consider signed Radon random measures on a separable, complete and locally compact metric space and study mean quadratic convergence with respect to vague topology on the space of measures. We prove sufficient conditions in order to obtain mean quadratic convergence. These results are based on some identification properties of signed Radon measures on the product space, also proved in this paper.

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