Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 18, No. 1, pp. 27-32 (2002)

Almost sure functional limit theorems in $L^2(]0,1[)$

József Túri

College of Nyíregyháza, Hungary.

Abstract: The almost sure version of Donsker's theorem is proved in $L^2(]0,1[)$. The almost sure functional limit theorem is obtained for the empirical process in $L^2(]0,1[)$.

Keywords: Functional limit theorem, almost sure central limit theorem, independent variables.

Classification (MSC2000): 60F17

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