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. ~
✦ LIBER ✦
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
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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.
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