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2013 Intricacies of dependence between components of multivariate Markov chains: weak Markov consistency and weak Markov copulae
Tomasz Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski
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Electron. J. Probab. 18: 1-21 (2013). DOI: 10.1214/EJP.v18-2238

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.

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Tomasz Bielecki. Jacek Jakubowski. Mariusz Niewęgłowski. "Intricacies of dependence between components of multivariate Markov chains: weak Markov consistency and weak Markov copulae." Electron. J. Probab. 18 1 - 21, 2013. https://doi.org/10.1214/EJP.v18-2238

Information

Accepted: 31 March 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1290.60072
MathSciNet: MR3040555
Digital Object Identifier: 10.1214/EJP.v18-2238

Subjects:
Primary: 60J27
Secondary: 60G55

JOURNAL ARTICLE
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