Maynooth University

Maynooth University ePrints and eTheses Archive

Maynooth University Library

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

[img] Download (156kB)

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;
Subjects: Science & Engineering > 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:

    Repository Staff Only(login required)

    View Item Item control page

    Document Downloads

    More statistics for this item...