Between the LIL and the LSL

Details Between the LIL and the LSL Between the LIL and the LSL

2010-02-22

arxiv.org/abs/1002.4121v1

Bernoulli 2010, Vol. 16, No. 1, 1-22

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ195 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ195

In two earlier papers, two of the present authors (A.G. and U.S.) extended Lai's [Ann. Probab. 2 (1974) 432--440] law of the single logarithm for delayed sums to a multiindex setting in which the edges of the $\mathbf{n}$th window grow like $|\mathbf {n}|^{\alpha}$, or with different $\alpha$'s, where the $\alpha$'s belong to $(0,1)$. In this paper, the edge of the $n$th window typically grows like $n/\log n$, thus at a higher rate than any power less than one, but not quite at the LIL-rate.

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