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arXiv · 0803.0727

A note on optimal probability lower bounds for centered random variables

Mark Veraar
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Abstract

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.

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Mark Veraar. 2008-04-24. A note on optimal probability lower bounds for centered random variables. https://arxiv.org/abs/0803.0727

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