Esscher变换和中心极限定理

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-04-11 DOI:10.1016/j.jfa.2025.110999

Sergey G. Bobkov , Friedrich Götze

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引用次数: 0

摘要

本文从中心极限定理的应用出发，研究了高维欧几里德空间上的Esscher变换。利用这个工具，我们从无限阶r nyi散度的角度探讨了i.i.d随机向量的归一化和的正态逼近的充分必要条件，推广了最近的一维结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Esscher transform and the central limit theorem

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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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis