Geodesic
An invariance principle in $L^2[0,1]$ for non stationary $\varphi$-mixing sequences
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 293-302

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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 $\varphi$-mixing random variables. Our result is not available in the $D(0,1)$-setting.
Classification : 60F17, 60G57
Keywords: reproducing kernel Hilbert space; random measure; invariance principle; $\varphi$-mixing 
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     title = {An invariance principle in $L^2[0,1]$ for non stationary $\varphi$-mixing sequences},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {293--302},
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Oliveira, Paulo Eduardo; Suquet, Charles. An invariance principle in $L^2[0,1]$ for non stationary $\varphi$-mixing sequences. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 293-302. http://geodesic.mathdoc.fr/item/CMUC_1995__36_2_a9/