A note on optimal probability lower bounds for centered random variables

Details A note on optimal probability lower bounds for centered random variables A note on optimal probability lower bounds for centered random variables

2008-03-05

arxiv.org/abs/0803.0727v2

Mathematics

Probability

Some typos corrected. To appear in Colloquium Mathematicum

Scientific paper

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.

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