Abstract: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.
Keywords: reproducing kernel Hilbert space, random measure, invariance principle, $\varphi $-mixing
AMS Subject Classification: 60F17, 60G57