Multivariate Markov Families of Copulas

19 Pages Posted: 8 Oct 2015

See all articles by Ludger Overbeck

Ludger Overbeck

University of Giessen

Wolfgang M. Schmidt

Frankfurt School of Finance & Management

Date Written: October 8, 2015

Abstract

For the Markov property of a multivariate process, a necessary and sufficient condition on the multi-dimensional 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 Darswo et al. (1992) 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

JEL Classification: C30, C22

Suggested Citation

Overbeck, Ludger and Schmidt, Wolfgang M., Multivariate Markov Families of Copulas (October 8, 2015). Available at SSRN: https://ssrn.com/abstract=2671164 or http://dx.doi.org/10.2139/ssrn.2671164

Ludger Overbeck

University of Giessen ( email )

Institut of Mathematics
Giessen, 35394
Germany

Wolfgang M. Schmidt (Contact Author)

Frankfurt School of Finance & Management ( email )

Adickesallee 32-34
Frankfurt am Main, 60322
Germany

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