On the Kolmogorov theorem (Q1600640)
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scientific article; zbMATH DE number 1756326
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Kolmogorov theorem |
scientific article; zbMATH DE number 1756326 |
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On the Kolmogorov theorem (English)
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16 June 2002
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A proof of the Doob's martingale convergence is given without resorting to the Doob's inequality for the number of intersections. The proof is based on a generalization of Kolmogorov's theorem to the \(L^p\)-case, which is also derived in the paper. This theorem immediately implies the well-known Lévy theorem.
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martingale convergence
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Doob's theorem
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Lévy's theorem
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