Limit theorems for random vectors with operator normalizations. II (Q2737022)
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scientific article; zbMATH DE number 1645093
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Limit theorems for random vectors with operator normalizations. II |
scientific article; zbMATH DE number 1645093 |
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11 September 2001
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operator normalized random vectors
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limit theorems
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martingales
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autoregression process
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strong law of large numbers
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operator normalization
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sub-Gaussian martingales
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Limit theorems for random vectors with operator normalizations. II (English)
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This article is the second part of the article [Theory Probab. Math. Stat. 61, 49-60 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 47-58 (1999; Zbl 0986.60021)]. The strong law of large numbers with operator normalization for sub-Gaussian martingales is studied and its application to the investigation of the asymptotic properties of many-dimensional autoregression processes is given. Conditions of fulfillment of the strong law of large numbers with operator normalization for vector sub-Gaussian martingales are proposed. In the one-dimensional case the sub-Gaussian martingales were studied by \textit{K. Azuma} [Tôhoku Math. J., II. Ser. 19, 357-367 (1967; Zbl 0178.21103)] and \textit{W. F. Stout} [``Almost sure convergence'' (1974; Zbl 0321.60022)].
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