%0 Journal Article
%T A note on optimal probability lower bounds for centered random variables
%A Mark Veraar
%J Mathematics
%D 2008
%I arXiv
%X In this note we obtain lower bounds for $\P(\xi\geq 0)$ and $\P(\xi>0)$ under assumptions on the moments of a centered random variable $\xi$. The obtained estimates are shown to be optimal and improve results from the literature. The results are applied to obtain probability lower bounds for second order Rademacher chaos.
%U http://arxiv.org/abs/0803.0727v2