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Gaussian functions / distributions / processes...
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History of the name "subexponential distribution" in probability
On the other hand, a subgaussian distribution is one whose moment generating function does not grow faster than the Gaussian-like function, so
$$
\mathbb{E}[e^{\lambda(X-\mathbb{E}[X])}] \le e^{\lambda … This guarantees tails that are no larger than Gaussian. …