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Quasi-infinitely divisible distributions

拟无限可分分布

基本信息

批准号：
419461105
负责人：
Professor Dr. Alexander Lindner
金额：
--
依托单位：
Institut für Finanzmathematik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2018
资助国家：
德国
起止时间：
2017-12-31 至 2020-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/419461105?language=en
关键词：
Quasi infinitely divisible distributions

项目摘要

A quasi-infinitely divisible distribution is a probability distribution whose characteristic function admits a Lévy-Khintchine type representation, however with a signed Lévy measure (the quasi-Lévy measure) rather than with a Lévy measure. Equivalently, a probability distribution is quasi-infinitely divisible if its characteristic function is the quotient of the characteristic functions of two infinitely divisible distributions. Quasi-infinitely divisible distributions appear naturally in the factorisation problem of infinitely divisible distributions. While infinitely divisible distributions form a well-studied class of probability distributions, much less is known about quasi-infinitely divisible distributions, and a systematic study of these distributions has only been initiated recently.The aim of this project is to deepen the understanding of quasi-infinitely divisible distributions. In particular, we intend to find conditions ensuring quasi-infinite divisibility of given distributions, and for a given quasi-infinitely distribution, to study its properties in terms of the quasi-Lévy measure. While much of the existing literature on quasi-infinitely divisible distributions at the moment is concerned only with the univariate case, we intend to study multivariate quasi-infinitely divisible distributions and in particular study if a Cramér-Wold device holds for this class of distributions. We shall also look for a natural connection of quasi-infinitely divisible distributions to stochastic processes.

准无限可分分布是一个概率分布，其特征函数允许一个Lévy-Khintchine型表示，但具有一个带符号的Lévy测度（准Lévy测度）而不是Lévy测度。等价地，一个概率分布是拟无限可分的，如果它的特征函数是两个无限可分分布的特征函数的商。拟无限可分分布自然地出现在无限可分分布的因子分解问题中。虽然无穷可分分布形成了一类研究得很好的概率分布，但对拟无穷可分分布的了解却少得多，对这些分布的系统研究只是最近才开始的，本项目的目的是加深对拟无穷可分分布的理解。特别是，我们打算找到确保给定分布的准无限整除性的条件，并且对于给定的准无限分布，研究其性质的准Lévy测度。虽然目前关于准无限可分分布的大部分现有文献只关注单变量的情况，但我们打算研究多变量准无限可分分布，特别是研究Cramér-Wold设备是否适用于这类分布。我们也将寻找一个自然的联系准无限可分分布随机过程。