Multivariate Markov Families of Copulas

Overbeck Ludger and Schmidt Wolfgang M.
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Overbeck Ludger: Justus-Liebig Universität Gießen, Institut of Mathematics, 35392 Gießen
Schmidt Wolfgang M.: Frankfurt School of Finance and Management, Sonnemannstr. 9-11, 60314 Frankfurt am Main

Dependence Modeling, 2015, vol. 3, issue 1, 13

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; Primary 60G07; secondary 60J05; 60J25; Markov process; copula; Chapman–Kolmogorov equation; Primary 60G07; secondary 60J05; 60J25 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:3:y:2015:i:1:p:13:n:11

DOI: 10.1515/demo-2015-0011

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