Positive invariance of polyhedrons and comparison of Markov reward models with different state spaces

Mourad Ahmane (1) , James Ledoux (2) , Laurent Truffet (3)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 Mines Nantes - Mines Nantes

In this paper, 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.

Domaines: Probabilités [math.PR]; Performance et fiabilité [cs.PF]

Mourad Ahmane, James Ledoux, Laurent Truffet. Positive invariance of polyhedrons and comparison of Markov reward models with different state spaces. Lecture notes in control and information sciences, 2006, 341, pp.153-160. ⟨hal-00447075⟩