A subexponential version of Cramer's theorem

Grégoire Ferré

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arXiv · 2206.05791

A subexponential version of Cramer's theorem

Grégoire Ferré

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Abstract

We consider the large deviations associated with the empirical mean of independent and identically distributed random variables under a subexponential moment condition. We show that non-trivial deviations are observable at a subexponential scale in the number of variables, and we provide the associated rate function, which is non-convex and is not derived from a Legendre-Fenchel transform. The proof adapts the one of Cramer's theorem to the case where the fluctuation is generated by a single variable. In particular, we develop a new tilting strategy for the lower bound, which leads us to introduce a condition on the second derivative of the moment generating function. Our results are illustrated by a couple of simple examples.

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BibTeX RIS

Grégoire Ferré. 2022-06-12. A subexponential version of Cramer's theorem. https://arxiv.org/abs/2206.05791

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