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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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Hoeffding's lemma for unbounded r.v with bounded exponential map

Let $X$ be a real r.v with $E[e^{\lambda X}] < \infty $ for all $\lambda \in [-c,c]$. Is it possible to get an Hoeffding's lemma like bound on $E[e^{\lambda(X-EX)}]$. That is, an upper bound: $$E[e^{ …
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