Precise asymptotics in the law of the iterated logarithm
Gut, Allan ; Sp{\u{a}}taru, Aurel
Ann. Probab., Tome 28 (2000) no. 1, p. 1870-1883 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Let $ X, X_1, X_2 \ldots$ be i.i.d. random variables with mean 0 and positive, finite variance $\sigma^2$, and set $S_n = X_1 + \cdots + X_n, n \geq 1$. Continuing earlier work related to strong laws, we prove the following analogs for the law of the iterated logarithm: [image] ¶ whenever $a_n = O(\sqrt{n}(\log \log n)^{-\gamma}$ for some $\gamma \geq 1/2$ (assuming slightly more than finite variance), and ¶ [image]
Publié le : 2000-10-14
Classification:  Tail probabilities of sums of i.i.d.random variables,,  law of the iterated logarithm,  Davis law,  Fuk–Nagaev type inequality,  60G50,  60E15,  60F15 
@article{1019160511,
     author = {Gut, Allan and Sp{\u{a}}taru, Aurel},
     title = {Precise asymptotics in the law of the iterated logarithm},
     journal = {Ann. Probab.},
     volume = {28},
     number = {1},
     year = {2000},
     pages = { 1870-1883},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019160511}
}

Gut, Allan; Sp{\u{a}}taru, Aurel. Precise asymptotics in the law of the iterated logarithm. Ann. Probab., Tome 28 (2000) no. 1, pp.  1870-1883. http://gdmltest.u-ga.fr/item/1019160511/