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On a question concerning condition numbers for Markov chains. (English) Zbl 1013.15005

An irreducible stochastic matrix S of order n with stationary vector π T , and the principal submatrix S (i) formed by deleting the ith row and column of S is considered. The relation

max 1in π i (I-S (i) ) -1 min 1jn (I-S (j) )

is obtained for it. An attainable lower bound on

max 1in π i (I-S (i) ) -1

is provided, and the case of its equality is discussed.

MSC:
15A51Stochastic matrices (MSC2000)
15A45Miscellaneous inequalities involving matrices
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
60J10Markov chains (discrete-time Markov processes on discrete state spaces)