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Keywords:
reproducing kernel Hilbert space; random measure; invariance principle; $\varphi$-mixing
reproducing kernel Hilbert space; random measure; invariance principle; $\varphi$-mixing
Summary:
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.
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