This note provides a basic description of subgaussianity, by defining $(\sigma, \rho)$-subgaussian random variables $X$ ($\sigma>0, \rho>0$) as those satisfying $\mathbb{E}(\exp(\lambda X))\leq \rho\exp(\frac{1}{2}\sigma^2\lambda^2)$ for any $\lambda\in\mathbb{R}$. The introduction of the parameter $\rho$ may be particularly useful for those seeking to refine bounds, or align results from different sources, in the analysis of stochastic processes and concentration inequalities.

翻译：本注记对次高斯性进行了基础性描述，将满足对任意 $\lambda\in\mathbb{R}$ 均有 $\mathbb{E}(\exp(\lambda X))\leq \rho\exp(\frac{1}{2}\sigma^2\lambda^2)$ 的随机变量 $X$ ($\sigma>0, \rho>0$) 定义为 $(\sigma, \rho)$-次高斯随机变量。参数 $\rho$ 的引入对于希望在随机过程分析和集中不等式研究中精确化界、或统一不同文献结果的学者可能具有特殊价值。