On norms in some class of exponential type Orlicz spaces of random variables

Abstract

A new characterization of the exponential type Orlicz spaces generated by the functions $\exp (|x{|}^p)-1$ ($p\ge 1$) is given. We define norms for centered random variables belonging to these spaces. We show equivalence of these norms with the Luxemburg norms. On the example of the Hoeffding inequality we present some application of these norms in a probabilistic context.

9 pages

References in corpus (1)

• The curse of dimensionality for numerical integration on general domains

Cited by in corpus (3)

• Sharper Sub-Weibull Concentrations
• Norms of sub-exponential random vectors
• Concentration of norms of random vectors with independent $p$-sub-exponential coordinates