A note on a limit theorem for differentiable mappings
A theorem of \textit{C. Hagwood} and \textit{H. Teicher} [Ann. Probab. 11, 1048-1050 (1983; Zbl 0519.60015)] states that the properly normalized random variables \(\max_{k\leq n}k^{-a}(X_ 1+...+X_ n)\) are asymptotically normal. Here \(0\leq a<1\), and \(X_ 1,X_ 2,..\). are i.i.d. random variables with strictly positive mean. The author points out that this and other results follow easily from the observation that under suitable conditions weak convergence of a sequence of random variables is preserved, if a differentiable function is applied to these r.v.
scientific article; zbMATH DE number 3917368