On the functional limits for sums of a function of partial sums

Details On the functional limits for sums of a function of partial sums On the functional limits for sums of a function of partial sums

2010-06-03

arxiv.org/abs/1006.0620v1

Statistics and Probability Letters 79 (2009) 1522--1527

Mathematics

Probability

Scientific paper

10.1016/j.spl.2009.03.011

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.

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