Zd值分布无穷可分性的Cramér–Wold装置

IF 1.5 2区数学 Q2 STATISTICS & PROBABILITY

Bernoulli Pub Date : 2022-05-01 DOI:10.3150/21-bej1386

David Berger, Alexandra H Lindner

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引用次数: 8

摘要

我们证明了Cramér–Wold装置适用于Zd值分布的无限可分性，即Zd值随机向量X的分布是无限可分的，当且仅当aTX的分布对所有a∈Rd都是无限可分割的，并且这反过来等价于aTX的分配对所有a≠N0的无限可分割性。证明这一点的一个关键工具是具有Zd值分布的特征函数的符号Lévy测度的Lévy-Khinchine型表示，前提是特征函数为零。

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A Cramér–Wold device for infinite divisibility of Zd-valued distributions

We show that a Cramér–Wold device holds for infinite divisibility of Zd-valued distributions, i.e. that the distribution of a Zd-valued random vector X is infinitely divisible if and only if the distribution of aTX is infinitely divisible for all a ∈ Rd, and that this in turn is equivalent to infinite divisibility of the distribution of aTX for all a ∈ N0. A key tool for proving this is a Lévy–Khintchine type representation with a signed Lévy measure for the characteristic function of a Zd-valued distribution, provided the characteristic function is zero-free.

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来源期刊

Bernoulli 数学-统计学与概率论

CiteScore

3.40

自引率

0.00%

发文量

116

审稿时长

6-12 weeks

期刊介绍： BERNOULLI is the journal of the Bernoulli Society for Mathematical Statistics and Probability, issued four times per year. The journal provides a comprehensive account of important developments in the fields of statistics and probability, offering an international forum for both theoretical and applied work. BERNOULLI will publish: Papers containing original and significant research contributions: with background, mathematical derivation and discussion of the results in suitable detail and, where appropriate, with discussion of interesting applications in relation to the methodology proposed. Papers of the following two types will also be considered for publication, provided they are judged to enhance the dissemination of research: Review papers which provide an integrated critical survey of some area of probability and statistics and discuss important recent developments. Scholarly written papers on some historical significant aspect of statistics and probability.