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Positive invariance of polyhedrons and comparison of Markov reward models with different state spaces. (English) Zbl 1132.93333
Commault, Christian (ed.) et al., Positive systems. Proceedings of the second multidisciplinary international symposium on positive systems: Theory and applications (POSTA 06), Grenoble, France, August 30 – September 1, 2006. Berlin: Springer (ISBN 3-540-34771-2/pbk). Lecture Notes in Control and Information Sciences 341, 153-160 (2006).
Summary: We discuss the comparison of expected rewards for discrete-time reward Markov chains with different state spaces. Necessary and sufficient conditions for such a comparison are derived. Due to the special nature of the introduced binary relation, a criterion may be formulated in terms of an inclusion of polyhedral sets. Then, algebraic and geometric forms are easily obtained from Haar’s lemma. Our results allow us to discuss some earlier results on the stochastic comparison of functions of Markov chains.
For the entire collection see [Zbl 1099.93002].

93C55 Discrete-time control/observation systems
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
93C05 Linear systems in control theory
93B27 Geometric methods