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Computing Entry-Wise Bounds of the Steady-State Distribution of a Set of Markov Chains

  • F. Ait Salaht
  • J. M. Fourneau
  • N. Pekergin
Conference paper

Abstract

We present two algorithms to find the component-wise upper and lower bounds of the steady-state distribution of an ergodic Markov chain. whose transition matrix\(\mathbf{M}\) is entry-wise larger than matrix \(\mathbf{L}\). The algorithms are faster than Muntz’s approach. They are based on the polyhedral theory developed by Courtois and Semal and on a new iterative algorithm which gives bounds of the steady-state distribution at each iteration.

Notes

Acknowledgments

This work was partially supported by a grant from CNRS GdR RO 2011.

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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.PRiSMUniversité de Versailles-Saint-QuentinVersaillesFrance
  2. 2.LACLUniversité Paris EstCréteilFrance

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