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On the perturbation of Markov chains with nearly transient states (1993)

Stewart, G. W.

Springer

Numerische Mathematik 65 (1993), S. 135-141

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ISSN: 0945-3245

Keywords: 15A51 ; 60J10

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary LetA be an irreducible stochastic matrix of the form $$A = \left( {\begin{array}{*{20}c} {A_{11} } & {E_{12} } \\ {A_{21} } & {A_{22} } \\ \end{array} } \right)$$ . IfE 12 were zero, the states corresponding toA 22 would be transient in the sense that if the steady state vectory T is partitioned conformally in the form (y 1 T y 2 T ) theny 2 T =0. IfE 12 is small, theny 2 T will be small, and the states are said to be nearly transient. In this paper it is shown that small relative perturbations inA 11,A 21, andA 22 though potentially larger thany 2 T induce only small relative perturbations iny 2 T .

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01385745

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