An Inversion Formula for Orlicz Norms and Sequences of Random Variables

Details An Inversion Formula for Orlicz Norms and Sequences of Random Variables An Inversion Formula for Orlicz Norms and Sequences of Random Variables

2012-04-05

arxiv.org/abs/1204.1242v1

Mathematics

Functional Analysis

11 pages

Scientific paper

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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