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arXiv · 1002.4121

Between the LIL and the LSL

Allan Gut·Fredrik Jonsson·Ulrich Stadtmüller
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Abstract

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 $|\mathbf {n}|^α$, or with different $α$'s, where the $α$'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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Allan Gut, Fredrik Jonsson, Ulrich Stadtmüller. 2010-02-22. Between the LIL and the LSL. https://doi.org/10.3150/09-bej195

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