Kirkland, Steve (2010) Column Sums and the Conditioning of the Stationary Distribution for a Stochastic Matrix. Operators and Matrices, 4. pp. 431443. ISSN 18463886
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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) = {AA 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:  
Use Licence:  This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BYNCSA). Details of this licence are available here 
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