Bochner's Theorem characterizes the the Fourier transform of a positive finite Borel measure on $\mathbb{R}$. This tells us, in principle, which functions can be characteristic function of a random variable. Is there any result that characterizes the (bilateral) Laplace transforms of measures on $\mathbb{R}$? That is, a way to determine whether a given function can be the moment generating function of a random variable?
2026-04-01 08:08:00.1775030880
Bochner-Type Theorem for MGF
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