A Simple Note on the Basic Properties of Subgaussian Random Variables
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914864671227904 |
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| author | Li, Yang |
| author_facet | Li, Yang |
| contents | This note provides a basic description of subgaussianity, by defining $(σ, ρ)$-subgaussian random variables $X$ ($σ>0, ρ>0$) as those satisfying $\mathbb{E}(\exp(λX))\leq ρ\exp(\frac{1}{2}σ^2λ^2)$ for any $λ\in\mathbb{R}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Simple Note on the Basic Properties of Subgaussian Random Variables Li, Yang Probability Optimization and Control Statistics Theory 60-01 G.3 This note provides a basic description of subgaussianity, by defining $(σ, ρ)$-subgaussian random variables $X$ ($σ>0, ρ>0$) as those satisfying $\mathbb{E}(\exp(λX))\leq ρ\exp(\frac{1}{2}σ^2λ^2)$ for any $λ\in\mathbb{R}$. 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. |
| title | A Simple Note on the Basic Properties of Subgaussian Random Variables |
| topic | Probability Optimization and Control Statistics Theory 60-01 G.3 |
| url | https://arxiv.org/abs/2407.07348 |