Stationary vectors of stochastic matrices subject to combinatorial constraints
Keyword(s):
Given a strongly connected directed graph D, let S_D denote the set of all stochastic matrices whose directed graph is a spanning subgraph of D. We consider the problem of completely describing the set of stationary vectors of irreducible members of S_D. Results from the area of convex polytopes and an association of each matrix with an undirected bipartite graph are used to derive conditions which must be satisfied by a positive probability vector x in order for it to be admissible as a stationary vector of some matrix in S_D. Given some admissible vector x, the set of matrices in S_D that possess x as a stationary vector is also characterised.
2017 ◽
Vol 27
(03)
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pp. 207-219
Keyword(s):
2018 ◽
Vol 29
(4)
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pp. 830-842
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2005 ◽
Vol 15
(05n06)
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pp. 997-1012
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2002 ◽
Vol 45
(3)
◽
pp. 617-630
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Keyword(s):