A Simple Note on the Basic Properties of Subgaussian Random Variables

This note provides a basic description of subgaussianity, by defining (σ, ρ)-subgaussian random variables X (σ>0, ρ>0) as those satisfying mathbbE(exp(λ X))≤ ρexp(frac12σ2λ2) for any λ∈ℝ. The introduction of the parameter ρ 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.