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 | 1998-10-28 | |
| dc.date.accessioned | 2026-07-07T05:26:38Z | |
| dc.date.available | 2026-07-07T05:26:38Z | |
| 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 tau_n and the positive increasing sequence a_n, we give necessary and sufficient conditions for the convergence of sum_{n=1}^infty tau_n P(|S_n|>t a_n) for all t>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 tau_n=1/n and a_n=(n log n)^{1/2} for n>1, 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/9810163 | |
| dc.identifier | http://arxiv.org/abs/math/9810163 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77619 | |
| dc.subject | Probability | |
| dc.subject | 60F05; 60F10; 60F15; 60E15 | |
| dc.title | A general Hsu-Robbins-Erdos type estimate of tail probabilities of sums of independent identically distributed random variables | |
| dc.type | text |