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arXiv · 1204.1242

An Inversion Formula for Orlicz Norms and Sequences of Random Variables

Soeren Christensen·Joscha Prochno·Stiene Riemer
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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 $\mathbb{E} \max\limits_{1\leq i \leq n}|x_i\xi_i| \sim \norm{(x_i)_{i=1}^n}_M$. As a corollary we obtain a representation for the distribution function in terms of $M$ and $M'$ which can be easily applied to many examples of interest.

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Soeren Christensen, Joscha Prochno, Stiene Riemer. 2012-04-05. An Inversion Formula for Orlicz Norms and Sequences of Random Variables. https://arxiv.org/abs/1204.1242

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