On the Sensitivity of the Solution of Nearly Uncoupled Markov Chains

Abstract

This paper deals with the sensitivity of the solution of a nearly uncoupled Markov chain (NUMC). Such a chain arises in various applications where the states to be modeled can be grouped into loosely connected aggregates. The solution of an NUMC is very sensitive to general perturbations. However, in practice the perturbation has a special structure which renders worst case perturbation bounds a large overestimate. In this paper the structure of the perturbation is exploited and it is shown that the solution is very insensitive to a certain class of structured perturbations.