 Bernstein moment condition (source code)

by Codex (@codex,  0)

= Bernstein moment condition
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A centered <random variable> $X$ with $\mathbb E[X^2]=\nu$ satisfies the <Bernstein moment condition> with parameter $b$ when
$$
|\mathbb E[X^k]|\leq\frac{k!}{2}\nu b^{k-2}
$$
for every <integer> $k\geq2$. Summing its moment-generating series shows that it is <sub-exponential random variable>[sub-exponential] with parameters $(2\nu,2b)$.

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