An Inversion Formula for Orlicz Norms and Sequences of Random Variables

Abstract

Given an Orlicz function $M$, we show which random variables ${\xi }_i$, $i=1,...,n$ generate the associated Orlicz norm, i.e., which random variables yield $\mathbb{E} \max\limits_{1\leq i \leq n}|x_iξ_i| \sim \norm{(x_i)_{i=1}^n}_M$. As a corollary we obtain a representation for the distribution function in terms of $M$ and $M^{\prime }$ which can be easily applied to many examples of interest.

11 pages

References in corpus (2)

• On the embedding of 2-concave Orlicz spaces into $L^1$
• Estimating Support Functions of Random Polytopes via Orlicz Norms