Electronic Journal of Probability

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

Tomasz Bielecki, Jacek Jakubowski, and Mariusz Niewęgłowski

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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.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 45, 21 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064270

Digital Object Identifier
doi:10.1214/EJP.v18-2238

Mathematical Reviews number (MathSciNet)
MR3040555

Zentralblatt MATH identifier
1290.60072

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60G55: Point processes

Keywords
Multivariate Markov chain compensator of random measure dependence marginal law Markov consistency Markov copulae

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Bielecki, Tomasz; Jakubowski, Jacek; Niewęgłowski, Mariusz. Intricacies of dependence between components of multivariate Markov chains: weak Markov consistency and weak Markov copulae. Electron. J. Probab. 18 (2013), paper no. 45, 21 pp. doi:10.1214/EJP.v18-2238. https://projecteuclid.org/euclid.ejp/1465064270


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