All Questions

Let $X$ be a centred random variable with variance $\sigma^2$, and whose moment-generating function exists in an open neighbourhood of the origin. Say that $X$ satisfies a 'Bernstein-type' MGF bound ...

Suppose that $X$ is a centered, $\mathbf{R}^d$-valued random variable such that for all $t \in \mathbf{R}^d$, there holds the bound $$\log \mathbf{E} \left[ \exp \langle t, X \rangle \right] \leqslant ...