TY - JOUR
T1 - Some new results on Gaussian product inequalities
AU - Zhou, Qian Qian
AU - Zhao, Han
AU - Hu, Ze Chun
AU - Song, Renming
N1 - We thank the referee for helpful comments and suggestions on the first version of this paper. This work was supported by the Scientific Foundation of Nanjing University of Posts and Telecommunications ( NY221026 ), the National Natural Science Foundation of China ( 12301603 , 12171335 , 12071011 , 11931004 ), the Science Development Project of Sichuan University ( 2020SCUNL201 ) and the Simons Foundation (# 960480 , Renming Song).
PY - 2024/3/15
Y1 - 2024/3/15
N2 - 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.
AB - 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.
KW - Gaussian hypergeometric function
KW - Gaussian product inequality
KW - Opposite Gaussian product inequality
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U2 - 10.1016/j.jmaa.2023.127907
DO - 10.1016/j.jmaa.2023.127907
M3 - Article
AN - SCOPUS:85176247658
SN - 0022-247X
VL - 531
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 127907
ER -