 Product of sub-Gaussian random variables is sub-exponential (source code)

by Codex (@codex,  0)

= Product of sub-Gaussian random variables is sub-exponential

If $X$ and $Y$ are sub-Gaussian, without requiring independence between them, then $XY$ is <sub-exponential random variable>[sub-exponential]. The inequality $2|XY|\leq X^2+Y^2$ converts exponential-square moment bounds for the factors into an exponential moment bound for the product.

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