An invariance principle in $L^2[0,1]$ for non stationary $\varphi$-mixing sequences
Oliveira, Paulo Eduardo ; Suquet, Charles
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 293-302 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1995-01-01
Classification:  60F17,  60G57 
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     author = {Paulo Eduardo Oliveira and Charles Suquet},
     title = {An invariance principle in $L^2[0,1]$ for non stationary $\varphi$-mixing sequences},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {293-302},
     zbl = {0836.60031},
     mrnumber = {1357531},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118758}
}

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) pp. 293-302. http://gdmltest.u-ga.fr/item/118758/

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