Esscher Transform and the Central Limit Theorem

2024/07/30 by Sergey G. Bobkov, Friedrich Götze, Bobkov, Sergey +1
Mathematics · #60E 60F #FOS: Mathematics #Mathematical functions and polynomials #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2407.20726

openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal approximation for normalized sums of i.i.d. random vectors in terms of the Rényi divergence of infinite order, extending recent one dimensional results.

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