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 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 with initial condition . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am31-2-3,
author = {W\l odzimierz Wysocki},
title = {Properties of the induced semigroup of an Archimedean copula},
journal = {Applicationes Mathematicae},
volume = {31},
year = {2004},
pages = {161-174},
zbl = {1051.62049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-2-3}
}
Włodzimierz Wysocki. Properties of the induced semigroup of an Archimedean copula. Applicationes Mathematicae, Tome 31 (2004) pp. 161-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-2-3/