We obtain lower bounds for ℙ(ξ ≥ 0) and ℙ(ξ > 0) under assumptions on the moments of a centered random variable ξ. The estimates obtained are shown to be optimal and improve results from the literature. They are then applied to obtain probability lower bounds for second order Rademacher chaos.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm113-2-5,
author = {Mark Veraar},
title = {A note on optimal probability lower bounds for centered random variables},
journal = {Colloquium Mathematicae},
volume = {111},
year = {2008},
pages = {231-240},
zbl = {1144.60014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm113-2-5}
}
Mark Veraar. A note on optimal probability lower bounds for centered random variables. Colloquium Mathematicae, Tome 111 (2008) pp. 231-240. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm113-2-5/