Let $\{S_n\}$ be the partial sums of a sequence of independent random variables and let $\{a_n\}$ be a nondecreasing, divergent real sequence. Necessary and sufficient conditions for $\lim \sup_{n\rightarrow\infty}S_n/a_n < \infty$ a.s. are given under mild conditions on $\{S_n\}$; these conditions do not involve the existence of any moments. These results are employed to widen the scope of the law of the iterated logarithm.
Publié le : 1980-04-14
Classification:
Almost sure convergence,
limit theorems,
law of iterated logarithm,
independent random variables,
almost sure stability,
60F15,
60G50
@article{1176994779,
author = {Tomkins, R. J.},
title = {Limit Theorems Without Moment Hypotheses for Sums of Independent Random Variables},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 314-324},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994779}
}
Tomkins, R. J. Limit Theorems Without Moment Hypotheses for Sums of Independent Random Variables. Ann. Probab., Tome 8 (1980) no. 6, pp. 314-324. http://gdmltest.u-ga.fr/item/1176994779/