Properties of the induced semigroup of an Archimedean copula

Włodzimierz Wysocki

Applicationes Mathematicae (2004)

  • Volume: 31, Issue: 2, page 161-174
  • ISSN: 1233-7234

Abstract

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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 d y / d x = v H ( y ) / x with initial condition ( d h / d x ) ( 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.

How to cite

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Włodzimierz Wysocki. "Properties of the induced semigroup of an Archimedean copula." Applicationes Mathematicae 31.2 (2004): 161-174. <http://eudml.org/doc/279247>.

@article{WłodzimierzWysocki2004,
abstract = {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.},
author = {Włodzimierz Wysocki},
journal = {Applicationes Mathematicae},
keywords = {phase flow; generator of phase flow; Archimedean copula; vector generator of Archimedean copula; projection of copula},
language = {eng},
number = {2},
pages = {161-174},
title = {Properties of the induced semigroup of an Archimedean copula},
url = {http://eudml.org/doc/279247},
volume = {31},
year = {2004},
}

TY - JOUR
AU - Włodzimierz Wysocki
TI - Properties of the induced semigroup of an Archimedean copula
JO - Applicationes Mathematicae
PY - 2004
VL - 31
IS - 2
SP - 161
EP - 174
AB - 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.
LA - eng
KW - phase flow; generator of phase flow; Archimedean copula; vector generator of Archimedean copula; projection of copula
UR - http://eudml.org/doc/279247
ER -

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