Properties of the induced semigroup of an Archimedean copula

• Autorzy: Włodzimierz Wysocki
• Języki publikacji: EN

Abstrakty

EN

It is shown that to every Archimedean copula H there corresponds a one-parameter semigroup of transformations of the interval [0,1]. If the elements of the semigroup are diffeomorphisms, then it determines a special function $v_{H}$ called the vector generator. Its knowledge permits finding a pseudoinverse y = h(x) of the additive generator of the Archimedean copula H by solving the differential equation $dy/dx = v_{H}(y)/x$ with initial condition $(dh/dx)(0) = -1$. Weak convergence of Archimedean copulas is characterized in terms of vector generators. A new characterization of Archimedean copulas is also given by using the notion of a projection of a copula.

Kategorie tematyczne

• 62H05: Characterization and structure theory
• 60E05: Distributions: general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2004
• Tom: 31
• Numer: 2
• Strony: 161-174

Daty

wydano

2004

Twórcy

autor

Włodzimierz Wysocki

• Institute of Foundations of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237 Warszawa, Poland

Identyfikatory

DOI

10.4064/am31-2-3