Probabilistic norms and convergence of random variables (Q1874427)
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scientific article; zbMATH DE number 1915601
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Probabilistic norms and convergence of random variables |
scientific article; zbMATH DE number 1915601 |
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Probabilistic norms and convergence of random variables (English)
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25 May 2003
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It is well-known that almost sure convergence is not metrizable. To circumvent this, the authors use the notion of probabilistic normed spaces, in particular Šerstnev spaces [see e.g. \textit{B. Schweizer} and \textit{A. Sklar}, ``Probabilistic metric spaces'' (1983; Zbl 0546.60010)] and construct a number of such spaces inducing different modes of convergence, as e.g., convergence in probability, \(L_p\)-convergence and almost sure convergence.
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convergence in probability
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almost sure convergence
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complete convergence
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probabilistic normed space
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probabilistic form
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