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Properties of the induced semigroup of an Archimedean copula

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Wysocki W.

Applicationes Mathematicae

2004

tom 31

nr 2

161-174

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.

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1 Applicationes Mathematicae

1 Wysocki W.

1 2004

Wyniki wyszukiwania

Properties of the induced semigroup of an Archimedean copula