A linear version of Dawson-G{\"a}rtner theorem -- Applications to Cram{\'e}r's theory

P Petit

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arXiv · 1909.02785

A linear version of Dawson-G{\"a}rtner theorem -- Applications to Cram{\'e}r's theory

P Petit

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Abstract

We prove a linear version of Dawson-G{\"a}rtner theorem: weak large deviation principles and the equality --s = p* between the negentropy and the Fenchel-Legendre transform of the pressure are preserved through linear projective limits. As a result, the equality --s = p* holds in great generality for empirical means of independent and identically distributed random variables (Cram{\'e}r's theory), e.g. in any measurable normed space, and even in any projective limit of such spaces. Eventually, we give an original example where --s is different from p* and discuss the dual equality.

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P Petit. 2019-09-06. A linear version of Dawson-G{\"a}rtner theorem -- Applications to Cram{\'e}r's theory. https://arxiv.org/abs/1909.02785

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