Displaying similar documents to “A note on optimal probability lower bounds for centered random variables”

Hypercontractivity of simple random variables

Paweł Wolff (2007)

Studia Mathematica

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The optimal hypercontractivity constant for a natural operator semigroup acting on a discrete finite probability space is established up to a universal factor. The two-point spaces are proved to be the extremal case. The constants obtained are also optimal in the related moment inequalities for sums of independent random variables.

On Bernoulli decomposition of random variables and recent various applications

François Germinet (2007-2008)

Séminaire Équations aux dérivées partielles

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In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.

On the product of triangular random variables

Mridula Garg, Sangeeta Choudhary, Saralees Nadarajah (2009)

Applicationes Mathematicae

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We derive the probability density function (pdf) for the product of three independent triangular random variables. It involves consideration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables.

Grüss-type bounds for covariances and the notion of quadrant dependence in expectation

Martín Egozcue, Luis García, Wing-Keung Wong, Ričardas Zitikis (2011)

Open Mathematics

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We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate...

On the Bennett–Hoeffding inequality

Iosif Pinelis (2014)

Annales de l'I.H.P. Probabilités et statistiques

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The well-known Bennett–Hoeffding bound for sums of independent random variables is refined, by taking into account positive-part third moments, and at that significantly improved by using, instead of the class of all increasing exponential functions, a much larger class of generalized moment functions. The resulting bounds have certain optimality properties. The results can be extended in a standard manner to (the maximal functions of) (super)martingales. The proof of the main result...

On d-finite tuples in random variable structures

Shichang Song (2013)

Fundamenta Mathematicae

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We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.