A note on optimal probability lower bounds for centered random variables

Mark Veraar

A note on optimal probability lower bounds for centered random variables

Probability 2008-04-24 v2 Optimization and Control

Authors: Mark Veraar

Abstract

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.

Keywords

probability theory upper bounds

Cite

@article{arxiv.0803.0727,
  title  = {A note on optimal probability lower bounds for centered random variables},
  author = {Mark Veraar},
  journal= {arXiv preprint arXiv:0803.0727},
  year   = {2008}
}

Comments

Some typos corrected. To appear in Colloquium Mathematicum

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