A Gaussian expectation product inequality

作者：Liu, Zhenxia; Wang, Zhi; Yang, Xiangfeng^*

来源：Statistics & Probability Letters, 2017, 124: 1-4.

DOI：10.1016/j.spl.2016.12.018

• Gaussian random vector
• Bochner's theorem
• Gaussian expectation product inequality

Let (X-1,. . ., X-n) be any n-dimensional centered Gaussian random vector, in this note the following expectation product inequality is proved:
E Pi (n)(j=1) f(j)( X-j) >= Pi (n)(j=1) Ef(j)(X-j)
for functionsh, 1 <= j <= n, taking the forms f(j)(x) = integral(infinity)(0) where mu(j), 1 <= j <= n, are finite positive measures. The motivation of studying such an inequality comes from the Gaussian correlation conjecture (which was recently proved) and the Gaussian moment product conjecture (which is still unsolved). Several explicit examples of such functions f(j) are given. The proof is built on characteristic functions of Gaussian random variables.

• 出版日期2017-5
• 单位宁波工程学院