Entropy and the discrete central limit theorem

Lampros Gavalakis and Ioannis Kontoyiannis

Stochastic Processes and their Applications, 2024, vol. 170, issue C

Abstract: A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of n independent and identically distributed lattice random variables and an appropriately discretised Gaussian, vanishes as n→∞.

Keywords: Central limit theorem; Entropy; Fisher information; Relative entropy; Bernoulli part decomposition; Lattice distribution; Convolution inequality (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104294

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