Some new results on Gaussian product inequalities

Qian Qian Zhou, Han Zhao, Ze Chun Hu, Renming Song

Research output: Contribution to journalArticlepeer-review

Abstract

The long-standing Gaussian product inequality (GPI) conjecture states that, for any centered Rn-valued Gaussian random vector (X1,…,Xn) and any positive reals α1,…,αn, E[∏j=1n|Xj|αj]≥∏j=1nE[|Xj|αj]. In this paper, we present some related inequalities for centered Rn-valued Gaussian random vector (X1,…,Xn) when {α1,…,αn} contains both positive and negative numbers.

Original languageEnglish (US)
Article number127907
JournalJournal of Mathematical Analysis and Applications
Volume531
Issue number2
DOIs
StatePublished - Mar 15 2024

Keywords

  • Gaussian hypergeometric function
  • Gaussian product inequality
  • Opposite Gaussian product inequality

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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