A note on optimal probability lower bounds for centered random variables
Abstract
Description
In this note we obtain lower bounds for $¶(ξ\geq 0)$ and $¶(ξ>0)$ under assumptions on the moments of a centered random variable $ξ$. 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.
Some typos corrected. To appear in Colloquium Mathematicum
Some typos corrected. To appear in Colloquium Mathematicum