On the Sensitivity of Nearly Uncoupled Markov Chains
Abstract
Nearly uncoupled Markov chains (aka nearly completely decomposable Markov
chains) arise in a variety of applications, where they model loosely
coupled systems. In such systems it may be difficult to determine the
transitions probabilities with high accuracy. This paper investigates the
sensitivity of the limiting distribution of the chain to perturbations in
the transition probabilities. The conclusion is that nearly uncoupled
Markov chains are quite sensitive to such perturbations but the
perturbation of the limiting distribution is not arbitrary.
(Also cross-referenced as UMIACS-TR-90-18)
Appeared in Numerical Solutions of Markov Chains, W. J. Stewart ed.,
Dekker, New York, 1990.