Moment ratio inequality of bivariate Gaussian distribution and three-dimensional Gaussian product inequality

被引：6
|
作者：
Russell, Oliver [1 ]
Sun, Wei [1 ]
机构：
[1] Concordia Univ, Dept Math & Stat, Montreal, PQ, Canada
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 527卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Gaussian product inequality; conjecture; Hypergeometric function; Combinatorial inequality; Sums-of-squares; Computational mathematics; PROOF; VARIABLES;
D O I：
10.1016/j.jmaa.2023.127410
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove the three-dimensional Gaussian product inequality (GPI) E[X12X22m2X2m3 3] >= E[X12]E[X22m2]E[X2m3 3] for any centered Gaussian random vector (X1, X2, X3) and m2, m3 is an element of N. We discover a novel inequality for the moment ratio |E[X 2m2+1X2m3+1 2 3]| E[X22m2X2m3 3] , which implies the 3D-GPI. The interplay between computing and hard analysis plays a crucial role in the proofs. (c) 2023 Elsevier Inc. All rights reserved.
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页数：27
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