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Dependence Modeling

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Multivariate Markov Families of Copulas

Ludger Overbeck / Wolfgang M. Schmidt
Published Online: 2015-10-26 | DOI: https://doi.org/10.1515/demo-2015-0011

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.

Keywords: Markov process; copula; Chapman–Kolmogorov equation

MSC:: Primary 60G07, secondary 60J05, 60J25

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About the article


Received: 2015-07-08

Accepted: 2015-10-09

Published Online: 2015-10-26


Citation Information: Dependence Modeling, Volume 3, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2015-0011.

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© 2015 Ludger Overbeck and Wolfgang M. Schmidt. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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