The limiting distribution of $\max_{1\leqslant k \leqslant n}S_k/k^{\frac{1}{2}}$ is derived via embedding. The theorem also applies to partial sums of certain dependent rv's. Thus the proof of the Darling and Erdos result is brought into line with recent literature; moreover, the scope of its applicability is greatly increased in regard both to dependence and moment assumptions.
Publié le : 1979-12-14
Classification:
Maximum of normalized sums,
normalized Brownian motion,
Uhlenbeck process,
extreme value distribution,
embedding,
dependent rv's,
60G50,
60B10,
60F05
@article{1176994906,
author = {Shorack, Galen R.},
title = {Extension of the Darling and Erdos Theorem on the Maximum of Normalized Sums},
journal = {Ann. Probab.},
volume = {7},
number = {6},
year = {1979},
pages = { 1092-1096},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994906}
}
Shorack, Galen R. Extension of the Darling and Erdos Theorem on the Maximum of Normalized Sums. Ann. Probab., Tome 7 (1979) no. 6, pp. 1092-1096. http://gdmltest.u-ga.fr/item/1176994906/