文章基本信息

标题：A topological proof of Sklar’s theorem in arbitrary dimensions
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作者：Fred Espen Benth ; Giulia Di Nunno ; Dennis Schroers 等
期刊名称：Dependence Modeling
电子版ISSN：2300-2298
出版年度：2022
卷号：10
期号：1
页码：22-28
DOI：10.1515/demo-2022-0103
语种：English
出版社：Walter de Gruyter GmbH
摘要：Copulas are appealing tools in multivariate probability theory and statistics. Nevertheless, the transfer of this concept to infinite dimensions entails some nontrivial topological and functional analytic issues, making a deeper theoretical understanding indispensable toward applications. In this short work, we transfer the well-known property of compactness of the set of copulas in finite dimensions to the infinite-dimensional framework. As an application, we prove Sklar’s theorem in infinite dimensions via a topological argument and the notion of inverse systems.
关键词：Copulas;Sklar’s theorem;topological inverse limits;infinite dimensions;compactness