Central limit theorem, weak law of large numbers for martingales in Banach spaces, and weak invariance principle -- a quantitative study (Q1343352)
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scientific article; zbMATH DE number 718689
| Language | Label | Description | Also known as |
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| English | Central limit theorem, weak law of large numbers for martingales in Banach spaces, and weak invariance principle -- a quantitative study |
scientific article; zbMATH DE number 718689 |
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Central limit theorem, weak law of large numbers for martingales in Banach spaces, and weak invariance principle -- a quantitative study (English)
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22 April 1997
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The main result of the paper is an estimate of proximity between expectations of smooth functionals of a Banach-space-valued martingale and of an infinitely divisible random element, respectively. A corresponding result is obtained for the \(B\)-valued partial sum process based on a martingale difference sequence. The author uses the well-known Lindeberg's operator method. Unfortunately, he does not cite a number of probability papers concerning the topic including the \(B\)-valued martingale setting.
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martingales in Banach spaces
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central limit theorem in Banach spaces
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Lindeberg's operator method
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martingale difference sequence
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