%0 Journal Article
%T On the functional limits for sums of a function of partial sums
%A Kamil Marcin Kosi¨˝ski
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.spl.2009.03.011
%X We derive a functional central limit theorem (fclt) for normalised sums of a function of the partial sums of independent and identically distributed random variables. In particular, we show, using a technique presented in Huang and Zhang (Electron. Comm. Probab. 12 (2007), 51--56), that the result from Qi (Statist. Probab. Lett. 62 (2003), 93--100), for normalised products of partial sums, can be generalised in this fashion to a fclt.
%U http://arxiv.org/abs/1006.0620v2