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    Column Sums and the Conditioning of the Stationary Distribution for a Stochastic Matrix


    Kirkland, Steve (2010) Column Sums and the Conditioning of the Stationary Distribution for a Stochastic Matrix. Operators and Matrices, 4. pp. 431-443. ISSN 1846-3886

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    Abstract

    For an irreducible stochastic matrix T, we consider a certain condition number (T), which measures the sensitivity of the stationary distribution vector to perturbations in T, and study the extent to which the column sum vector for T provides information on (T). Specifically, if cT is the column sum vector for some stochastic matrix of order n, we define the set S(c) = {A|A is an n × n stochastic matrix with column sum vector cT }. We then characterise those vectors cT such that (T) is bounded as T ranges over the irreducible matrices in S(c); for those column sum vectors cT for which  is bounded, we give an upper bound on  in terms of the entries in cT , and characterise the equality case.

    Item Type: Article
    Keywords: Stochastic matrix; Stationary distribution; Condition number;
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 2194
    Depositing User: Professor Steve Kirkland
    Date Deposited: 15 Oct 2010 11:07
    Journal or Publication Title: Operators and Matrices
    Publisher: Elements d.o.o. Publishing House
    Refereed: Yes
    URI:

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