Geodesic
A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain
The electronic journal of linear algebra, Tome 11 (2004), pp. 168-179.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For an irreducible stochastic matrix T of order n, a certain condition number $u*j(T )$ that measures the sensitivity of the j-th entry of the corresponding stationary distribution under perturbation of T is considered. A lower bound on u*j is produced in terms of the directed graph of T , and the case of equality is characterized in that lower bound. Also all of the directed graphs D are characterized such that $u*j(T )$ is bounded from above as T ranges over the set of irreducible stochastic matrices having directed graph D. For those D for which u*j is bounded, a tight upper bound is given on u*j in terms of information contained in D.
Classification : 15A51, 15A18, 65F35, 60J10
Keywords: stochastic matrix, Markov chain, stationary vector, condition number, directed graph 
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     author = {Kirkland, S.},
     title = {A combinatorial approach to the conditioning of a single entry in the stationary distribution for a {Markov} chain},
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Kirkland, S. A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain. The electronic journal of linear algebra, Tome 11 (2004), pp. 168-179. http://geodesic.mathdoc.fr/item/ELA_2004__11__a8/