A note on optimal probability lower bounds for centered random variables

Volume 113 / 2008

Mark Veraar Colloquium Mathematicum 113 (2008), 231-240 MSC: Primary 60E15. DOI: 10.4064/cm113-2-5


We obtain lower bounds for ${\mathbb P}(\xi\geq 0)$ and ${\mathbb P}({\xi> 0})$ under assumptions on the moments of a centered random variable $\xi$. 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.


  • Mark VeraarInstitut für Analysis
    Universität Karlsruhe (TH)
    D-76128 Karlsruhe, Germany

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