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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 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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