Exponential inequalities in probability spaces revisited

2023/05/31 by Barki, Ali, Bobkov, Sergey G., Dagher, Esther Bou +1
#FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.00209

Abstract

We revisit several results on exponential integrability in probability spaces and derive some new ones. In particular, we give a quantitative form of recent results by Cianchi-Musil and Pick in the framework of Moser-Trudinger-type inequalities, and recover Ivanisvili-Russell's inequality for the Gaussian measure. One key ingredient is the use of a dual argument, which is new in this context, that we also implement in the discrete setting of the Poisson measure on integers.

Related

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• An extension of the Beckner's type Poincar 'e inequality to convolution\n measures on abstract Wiener spaces
• Tail inequalities for restricted classes of discrete random variables