Invariance principles with logarithmic averaging for martingales (Q2754990)
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scientific article; zbMATH DE number 1668839
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariance principles with logarithmic averaging for martingales |
scientific article; zbMATH DE number 1668839 |
Statements
5 November 2001
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almost sure central limit theorem
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Invariance principles with logarithmic averaging for martingales (English)
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The author proves an almost sure central limit theorem for discrete unidimensional martingales; this is a generalization in the martingale framework of previous results by \textit{B. Rodzyik} and \textit{Z. Rychlik} [Ann. Inst. Henri Poncaré, Probab. Stat. 30, No. 1, 1-11 (1994; Zbl 0793.60023)] for independent and nonidentically distributed r.v.s. Then the author derives a weighted strong law of large numbers for which he specifies both weak and strong rate of convergence; this is an extension of works by \textit{M. Csörgő} and \textit{L. Horváth} [Math. Proc. Camb. Philos. Soc. 112, No. 1, 195-205 (1992; Zbl 0766.60038)].
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