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Integral analogues of almost sure limit theorems

✍ Scribed by Alexey Chuprunov; István Fazekas


Publisher
Springer Netherlands
Year
2005
Tongue
English
Weight
220 KB
Volume
50
Category
Article
ISSN
0031-5303

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📜 SIMILAR VOLUMES


On almost sure max-limit theorems
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We prove an almost sure version of a maximum limit theorem using logarithmic means and show that essentially only logarithmic means work as it is the case for almost sure central limit theorems. ~

Almost sure central limit theorems for r
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## Abstract A general almost sure limit theorem is presented for random fields. It is applied to obtain almost sure versions of some (functional) central limit theorems. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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We show that the accumulated gain Sn and the maximal gain Mn in n St. Petersburg games satisfy almost sure limit theorems with nondegenerate limits, even though ordinary asymptotic distributions do not exist for Sn and Mn with any numerical centering and norming sequences.