Integral generators of Archimedean n-copulas

ABSTRACT

We introduce two algebraic structures induced by an Archimedean n-copula: a one-parameter group of transformations and a one-parameter local group of transformations. We then study the natural functional characteristics (integral generators) of these structures. We discuss differential equations joining the integral generators and the additive generators of copulas. We show that the algebraic structures can be recovered by using a certain parametric family of differential equations. Finally, we give some applications of integral generators, and we indicate potential applications of the algebraic and analytical results obtained.

KEYWORDS:

• Archimedean n-copula
• induced algebraic structure
• integral generator

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62H20

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Włodzimierz Wysocki  http://orcid.org/0000-0001-6071-7482