Let $X_i \geq 0$ be i.i.d. random variables with $E(X_i) = \infty$. Then for suitable functions $\varphi$ we have $\overline{\varphi(X)}/\varphi(\bar{X}) \rightarrow 0$ a.s. We give some applications of this result.
Publié le : 1984-02-14
Classification:
Sums of random variables,
nonexistence of moments,
moments,
60F99,
62G99,
62F99
@article{1176993388,
author = {Chen, Jeesen and Rubin, Herman},
title = {A Note on the Behavior of Sample Statistics when the Population Mean is Infinite},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 256-261},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993388}
}
Chen, Jeesen; Rubin, Herman. A Note on the Behavior of Sample Statistics when the Population Mean is Infinite. Ann. Probab., Tome 12 (1984) no. 4, pp. 256-261. http://gdmltest.u-ga.fr/item/1176993388/