Intricacies of dependence between components of multivariate Markov chains: weak Markov consistency and weak Markov copulae

Tomasz R. Bielecki (Illinois Institute of Technology)
Jacek Jakubowski (University of Warsaw and Warsaw University of Technology)
Mariusz Niewęgłowski (Warsaw University of Technology)


In this paper we examine the problem of existence and construction of multivariate Markov chains such that their components are Markov chains with given laws. Specifically, we provide sufficient and necessary conditions, in terms of semimartingale characteristics, for a component of a multivariate Markov chain to be a Markov chain in its own filtration - a property called weak Markov consistency. Accordingly, we introduce and discuss the concept of weak Markov copulae. Finally, we examine relationship between the concepts of weak Markov consistency and weak Markov copulae, and the corresponding strong versions of these concepts.

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Pages: 1-21

Publication Date: March 31, 2013

DOI: 10.1214/EJP.v18-2238


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