Darling-Erdős theorems for normalized sums of i.i.d. variables close to a stable law
Bertoin, Jean
Ann. Probab., Tome 26 (1998) no. 1, p. 832-852 / Harvested from Project Euclid
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Let $\xi, \xi_1, \dots$ be i.i.d. real-valued random variables and $S_n = \xi_1 + \dots + \xi_n$. In the case when the distribution of $\xi$ is close to a stable $(\alpha)$ law for some $\alpha \epsilon (0, 1) \bigcup (1, 2)$, we investigate the asymptotic behavior in distribution of the maximum of normalized sums, $\max_{k=1,\dots,n} k^{-1/\alpha}S_k$. This completes the Darling-Erdös limit theorem for the case $\alpha = 2$.
Publié le : 1998-04-14
Classification:  Stable Lévy process,  normalized maximum,  Darling-Erdös theorem,  60J30,  60F05,  60G10 
@article{1022855652,
     author = {Bertoin, Jean},
     title = {Darling-Erd\H os theorems for normalized sums of i.i.d.
		 variables close to a stable law},
     journal = {Ann. Probab.},
     volume = {26},
     number = {1},
     year = {1998},
     pages = { 832-852},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1022855652}
}

Bertoin, Jean. Darling-Erdős theorems for normalized sums of i.i.d.
		 variables close to a stable law. Ann. Probab., Tome 26 (1998) no. 1, pp.  832-852. http://gdmltest.u-ga.fr/item/1022855652/