Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables
The series $\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$ is studied, where $S_n$ are the sums of independent equally distributed random variables, $τ_n$ is a sequence of nonnegative numbers, $α > 0$, and $ɛ > 0$ is an arbitrary positive number. For...
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| Datum: | 1993 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5866 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | The series $\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$ is studied, where $S_n$ are the sums of independent equally distributed random variables, $τ_n$ is a sequence of nonnegative numbers, $α > 0$, and $ɛ > 0$ is an arbitrary positive number. For a broad class of sequences $τ_n$, the necessary and sufficient conditions are established for the convergence of this series for any $ɛ > 0$. |
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