Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order
Probability
2026-04-30 v1 Information Theory
math.IT
Statistics Theory
Machine Learning
Statistics Theory
Abstract
We prove that any random variable whose moment generating function is point-wise upper bounded by that of must be dominated by in convex order, meaning for all convex . Equality is attained by taking and .
Cite
@article{arxiv.2604.26819,
title = {Sharp One-Dimensional Sub-Gaussian Comparison in Convex Order},
author = {Yihan Zhang},
journal= {arXiv preprint arXiv:2604.26819},
year = {2026}
}