Some results on two-sided LIL behavior
| dc.creator | Einmahl, Uwe | |
| dc.creator | Li, Deli | |
| dc.date | 2005-07-22 | |
| dc.date.accessioned | 2026-07-07T05:21:55Z | |
| dc.date.available | 2026-07-07T05:21:55Z | |
| dc.description | Let {X,X_n;n\geq 1} be a sequence of i.i.d. mean-zero random variables, and let S_n=\sum_{i=1}^nX_i,n\geq 1. We establish necessary and sufficient conditions for having with probability 1, 0<lim sup_{n\to \infty}|S_n|/\sqrtnh(n)<\infty, where h is from a suitable subclass of the positive, nondecreasing slowly varying functions. Specializing our result to h(n)=(\log \log n)^p, where p>1 and to h(n)=(\log n)^r, r>0, we obtain analogues of the Hartman-Wintner LIL in the infinite variance case. Our proof is based on a general result dealing with LIL behavior of the normalized sums {S_n/c_n;n\ge 1}, where c_n is a sufficiently regular normalizing sequence. | |
| dc.description | Published at http://dx.doi.org/10.1214/009117905000000198 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0507462 | |
| dc.identifier | http://arxiv.org/abs/math/0507462 | |
| dc.identifier | Annals of Probability 2005, Vol. 33, No. 4, 1601-1624 | |
| dc.identifier | doi:10.1214/009117905000000198 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75866 | |
| dc.subject | Probability | |
| dc.subject | 60F15, 60G50 (Primary) | |
| dc.title | Some results on two-sided LIL behavior | |
| dc.type | text |