2023 / December Volume 18 No.4
Large deviations of sums mainly due to just one summand for super-heavy tailed distributions
Published Date |
2023 / December
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Title | Large deviations of sums mainly due to just one summand for super-heavy tailed distributions |
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Pagination | 437-449 |
Abstract | Recently, Pinelis (2022) gave careful consideration that large deviations of the sums of independent and identically distributed random variables with power-like tails of index $\alpha\in(0,2)$ are mainly due to just one of the summands. In this article, we show a corresponding result for $\alpha=0$, which is constructed by super-heavy tailed distributions. The proof uses a property of slow variation investigated by Bojanic and Seneta (1971). It is applied to not only the log-Pareto distribution but also the distribution of the super-Petersburg game. |
DOI | |
AMS Subject Classification |
60G50, 60E05
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Received |
2023-10-28
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