Some Improvements for the Computation of the Steady-State Distribution of a Markov Chain by Monotone Sequences of Vectors

  • Jean-Michel Fourneau
  • Franck Quessette
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7314)

Abstract

We present several new improvements for a recently published algorithm [5] for computing the steady-state distribution of a finite ergodic Markov chain, which has a proved monotone convergence under some structural constraints on the matrix. We show how to accommodate infinite state space and that the structural constraints of the algorithm are consistent with Pagerank matrix. We present how to combine this algorithm with stochastic comparison theory to numerically obtain bounds and we prove a pre-processing of the matrix which allows to alleviate the structural constraints. The approaches are illustrated through several small examples.

Keywords

Markov Chain State Space Structural Constraint Stochastic Matrix Stochastic Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jean-Michel Fourneau
    • 1
  • Franck Quessette
    • 1
  1. 1.PRiSMUniversité de Versailles-Saint-Quentin, CNRS UMR 8144, UniverSudVersaillesFrance

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