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Digraph-based Conditioning for Markov Chains

  • Invited Session: Nonnegative Matrices
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Positive Systems

Part of the book series: Lecture Notes in Control and Information Science ((LNCIS,volume 294))

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Abstract

Let T be an irreducible stochastic matrix, so that we can consider T to be the transition matrix for a Markov chain; one of the central quantities of interest for that chain is the stationary vector for T, i.e. the left Perron vector π t for T, normalized so that its entries sum to 1. It is well-known that in the case that T is primitive then the iterates of the chain converge to π t.

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Luca Benvenuti Alberto De Santis Lorenzo Farina

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Kirkland, S.J. Digraph-based Conditioning for Markov Chains. In: Benvenuti, L., De Santis, A., Farina, L. (eds) Positive Systems. Lecture Notes in Control and Information Science, vol 294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44928-7_29

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  • DOI: https://doi.org/10.1007/978-3-540-44928-7_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40342-5

  • Online ISBN: 978-3-540-44928-7

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