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Iterative component-wise bounds for the steady-state distribution of a Markov chain


Jean-Michel Fourneau, PRiSM, U. Versailles St-Quentin, CNRS UMR 8144, UniverSud, Paris, France.



We prove new iterative algorithms to provide component-wise bounds of the steady-state distribution of an irreducible and aperiodic Markov chain. These bounds are based on simple properties of (max,+) and (min,+) sequences. The bounds are improved at each iteration. Thus, we have a clear trade-off between tightness of the bounds (some algorithms converge to the true solution) and computation times. Copyright © 2011 John Wiley & Sons, Ltd.