Orlicz norms of sequences of random variables

Yehoram Gordon, Alexander Litvak, Carsten Schütt, Elisabeth Werner

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

Let fi, i = 1, ..., n, be copies of a random variable f and let N be an Orlicz function. We show that for every x ∈ ℝn the expectation E∥(xifi)i=1n∥N is maximal (up to an absolute constant) if fi, i = 1, ..., n, are independent. In that case we show that the expectation E∥(xi fi)i=1n∥ N is equivalent to ∥x∥M, for some Orlicz function M depending on N and on distribution of f only. We provide applications of this result.

Original languageEnglish (US)
Pages (from-to)1833-1853
Number of pages21
JournalAnnals of Probability
Volume30
Issue number4
DOIs
StatePublished - Oct 2002

Keywords

  • Orlicz norms
  • Random variables

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