  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.
