Esscher transform and the central limit theorem

Sergey G. Bobkov; Friedrich Götze

doi:10.1016/j.jfa.2025.110999

Esscher transform and the central limit theorem

Sergey G. Bobkov
, Friedrich Götze

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	110999
Journal	Journal of Functional Analysis
Volume	289
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2025.110999
State	Published - Sep 1 2025

Bibliographical note

Publisher Copyright:
© 2025 The Authors

Keywords

Central limit theorem
Esscher transform
Rényi divergence

Publisher link

10.1016/j.jfa.2025.110999

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AB - 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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KW - Rényi divergence

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Esscher transform and the central limit theorem

Abstract

Bibliographical note

Keywords

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