A Simple Note on the Basic Properties of Subgaussian Random Variables

2024/07/10 by Yang Li, Li, Yang · 1 citation
Mathematics · #60-01 #Advanced Statistical Methods and Models #FOS: Mathematics #G.3 #Optimization and Control (math.OC) #Probability (math.PR) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2407.07348

openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This note provides a basic description of subgaussianity, by defining (σ, ρ)-subgaussian random variables X (σ>0, ρ>0) as those satisfying 𝔼(exp(λX))≤ ρexp((1)/(2)σ²λ²) 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.

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