Multivariate Markov Families of Copulas

Ludger Overbeck; Wolfgang M. Schmidt

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 159-171, electronic only
  • ISSN: 2300-2298

Abstract

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For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples are also given.

How to cite

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Ludger Overbeck, and Wolfgang M. Schmidt. "Multivariate Markov Families of Copulas." Dependence Modeling 3.1 (2015): 159-171, electronic only. <http://eudml.org/doc/275965>.

@article{LudgerOverbeck2015,
abstract = {For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples are also given.},
author = {Ludger Overbeck, Wolfgang M. Schmidt},
journal = {Dependence Modeling},
keywords = {Markov process; copula; Chapman–Kolmogorov equation; Markov processes; copulas; Chapman-Kolmogorov equation},
language = {eng},
number = {1},
pages = {159-171, electronic only},
title = {Multivariate Markov Families of Copulas},
url = {http://eudml.org/doc/275965},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Ludger Overbeck
AU - Wolfgang M. Schmidt
TI - Multivariate Markov Families of Copulas
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 159
EP - 171, electronic only
AB - For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples are also given.
LA - eng
KW - Markov process; copula; Chapman–Kolmogorov equation; Markov processes; copulas; Chapman-Kolmogorov equation
UR - http://eudml.org/doc/275965
ER -

References

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