A general Hsu-Robbins-Erdos type estimate of tail probabilities of sums of independent identically distributed random variables
| dc.creator | Pruss, Alexander R. | |
| dc.date | 2002-04-02 | |
| dc.date.accessioned | 2026-07-07T04:47:23Z | |
| dc.date.available | 2026-07-07T04:47:23Z | |
| dc.description | Let $X_1,X_2,...$ be a sequence of independent and identically distributed random variables, and put $S_n=X_1+...+X_n$. Under some conditions on the positive sequence $τ_n$ and the positive increasing sequence $a_n$, we give necessary and sufficient conditions for the convergence of $\sum_{n=1}^\infty τ_n P(|S_n|\ge εa_n)$ for all $ε>0$, generalizing Baum and Katz's (1965) generalization of the Hsu-Robbins-Erdos (1947, 1949) law of large numbers, also allowing us to characterize the convergence of the above series in the case where $τ_n=n^{-1}$ and $a_n=(n\log n)^{1/2}$ for $n\ge 2$, thereby answering a question of Spataru. Moreover, some results for non-identically distributed independent random variables are obtained by a recent comparison inequality. Our basic method is to use a central limit theorem estimate of Nagaev (1965) combined with the Hoffman-Jorgensen inequality (1974). | |
| dc.identifier | https://arxiv.org/abs/math/0204022 | |
| dc.identifier | http://arxiv.org/abs/math/0204022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63693 | |
| dc.subject | Probability | |
| dc.subject | 60F05; 60F10; 60F15 | |
| dc.title | A general Hsu-Robbins-Erdos type estimate of tail probabilities of sums of independent identically distributed random variables | |
| dc.type | text |