Conditional Markov chains: Properties, construction and structured dependence

Tomasz R. Bielecki, Jacek Jakubowski and Mariusz Niewęgłowski

Stochastic Processes and their Applications, 2017, vol. 127, issue 4, 1125-1170

Abstract: In this paper we contribute to the theory of conditional Markov chains (CMCs) that take finitely many values and that admit intensity. We provide a method for constructing a CMC with given intensity and with given conditional initial law, and which is also a doubly stochastic Markov chain. We provide a martingale characterization for such process, and we discuss other useful properties. We define and give sufficient and necessary conditions for strong Markovian consistency and weak Markovian consistency of a multivariate CMC. We use these results to model structured dependence between univariate CMCs, that is, to model a multivariate CMC whose components are univariate CMCs with given laws. An example of potential application of our theory is presented.

Keywords: Conditional Markov chain; Doubly stochastic Markov chain; Compensator of a random measure; Change of probability measure (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:4:p:1125-1170

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DOI: 10.1016/j.spa.2016.07.010

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