On Multivariate Quasi-infinitely Divisible Distributions
On Multivariate Quasi-infinitely Divisible Distributions
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DOI：
10.1007/978-3-030-83309-1_6
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
David Berger;Merve Kutlu;A. Lindner
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文献类型：
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作者：
David Berger;Merve Kutlu;A. Lindner
一个拟无限可分分布是一个概率分布μ on，它的特征函数可以写成μ on上两个无限可分分布的特征函数之商，等价地，它可以被刻画为这样一个概率分布，它的特征函数具有一个Lévy-Khintchine型表示，该表示具有一个“符号Lévy测度”，即所谓的拟Lévy测度，而不是Lévy测度。Lindner，Pan和Sato对单变量情况下的此类分布进行了系统研究（Trans Am Math Soc 370：8483-8520，2018）。本文的目的是收集多元拟无限可分分布的一些已知结果，并将一些单变量结果推广到多元情形。特别是，弱收敛，时刻和支持性能的条件被认为是。一个特别强调的是这样的分布，特别是对值准无限可分分布的例子。
A quasi-infinitely divisible distribution onis a probability distributionμonwhose characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible distributions on. Equivalently, it can be characterised as a probability distribution whose characteristic function has a Lévy–Khintchine type representation with a “signed Lévy measure”, a so called quasi–Lévy measure, rather than a Lévy measure. A systematic study of such distributions in the univariate case has been carried out in Lindner, Pan and Sato (Trans Am Math Soc 370:8483–8520, 2018). The goal of the present paper is to collect some known results on multivariate quasi-infinitely divisible distributions and to extend some of the univariate results to the multivariate setting. In particular, conditions for weak convergence, moment and support properties are considered. A special emphasis is put on examples of such distributions and in particular on-valued quasi-infinitely divisible distributions.