A note on optimal probability lower bounds for centered random variables

2008/03/05 by Mark Veraar, Veraar, Mark
Decision Sciences · Economics, Econometrics and Finance · #60E15 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Probability and Risk Models #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0803.0727

openalex publication_date 2008/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we obtain lower bounds for ¶(ξ≥ 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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