The Entropy Method in Large Deviation Theory

TL;DR

This paper demonstrates the effectiveness of the entropy method in proving key results in large deviation theory, including classical theorems and an enhanced version of Sanov's theorem.

Contribution

It provides a comprehensive review and new strengthened proof of Sanov's theorem using the entropy method, unifying and advancing theoretical understanding.

Findings

Entropy proofs for Cramer's, G"artner--Ellis, and Sanov's theorems

Strengthened Sanov's theorem to a strong version

Unified approach via the entropy method

Abstract

This paper illustrates the power of the entropy method in addressing problems from large deviation theory. We provide and review entropy proofs for most fundamental results in large deviation theory, including Cramer's theorem, the G\"artner--Ellis theorem, and Sanov's theorem. Moreover, by the entropy method, we also strengthen Sanov's theorem to the strong version.