## 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. (Β© 2003 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
Almost-Sure Central Limit Theorem for Directed Polymers and Random Corrections
β Scribed by C. Boldrighini; R.A. Minlos; A. Pellegrinotti
- Publisher
- Springer
- Year
- 1997
- Tongue
- English
- Weight
- 335 KB
- Volume
- 189
- Category
- Article
- ISSN
- 0010-3616
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## Abstract Let __X__, __X__~1~, __X__~2~, β¦ be i.i.d. random variables with nondegenerate common distribution function __F__, satisfying __EX__ = 0, __EX__^2^ = 1. Let __X~i~__ and __M~n~__ = max{__X~i~__, 1 β€ __i__ β€ __n__ }. Suppose there exists constants __a~n~__ > 0, __b~n~__ β __R__ and a non
We prove an almost sure central limit theorem for some multidimensional stochastic algorithms used for the search of zeros of a function and known to satisfy a central limit theorem. The almost sure version of the central limit theorem requires either a logarithmic empirical mean (in the same way as