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Intricacies of dependence between components of multivariate Markov chains: weak Markov consistency and weak Markov copulae. (English) Zbl 1290.60072

Authors’ abstract: 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.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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