Essential Closures and Supports of Multivariate Copulas
Pongpol Ruankong, Songkiat Sumetkijakan
TL;DR
This paper introduces a generalized concept of essential closures to characterize the supports of multivariate copulas, providing explicit formulas and stronger conditions in certain cases.
Contribution
It extends the notion of essential closures for multivariate copulas and derives explicit support formulas and improved necessary conditions in specific scenarios.
Findings
Derived explicit formulas for copula supports using essential closures.
Established stronger necessary conditions for supports in special cases.
Generalized the geometric framework for analyzing multivariate copulas.
Abstract
We generalize the notion of essential closures which is used in formulating a geometric necessary condition for a set to be the support of a multivariate copula. Furthermore, in some special cases, we derive an explicit formula of the support in terms of essential closures and obtain a stronger necessary condition.
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