Sensitivity of finite Markov chains under perturbation

E. Seneta

Statistics & Probability Letters, 1993, vol. 17, issue 2, 163-168

Abstract: Meyer (1992) has developed inequalities in terms of the non-unit eigenvalues [lambda]j, j = 2,...,n, of a stochastic matrix P containing a single irreducible set of states, for the condition number maxa#ij, where A# = {a#ij} is the group generalized inverse of A = I - P. In this note we derive, succinctly, analogous inequalities for the alternative condition number, the ergodicity coefficient [tau]1(A#), using the properties of ergodicity coefficients: (min1 - [lambda]j)-1

Keywords: Condition; number; ergodicity; coefficients; eigenvalues; group; inverse; sensitivity; perturbation; of; Markov; chains; fundamental; matrix; stochastic; matrix; stationary; distribution (search for similar items in EconPapers)
Date: 1993
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Citations: View citations in EconPapers (8)

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