On convergence of series of independent random variables (Q2770344)
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scientific article; zbMATH DE number 1703160
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On convergence of series of independent random variables |
scientific article; zbMATH DE number 1703160 |
Statements
24 September 2003
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convergence in probability
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tail series
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independent random variables
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weak law of large numbers
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almost sure convergence
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On convergence of series of independent random variables (English)
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Let \((X_n, n\geq 1) \) be a sequence of independent random variables and let the series \(\sum_{i=1}^{\infty} X_i\) converge almost surely. Define \(T_n =\sum _{i=n}^\infty X_i\), \(n\geq 1\). Conditions are provided so that \(\sup_{k\geq n} |T_k |/ b_n \to 0\) in probability for a given sequence of positive constants \((b_n, n \geq 1)\).
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