Limit Behaviour of Upper and Lower Expected Time Averages in Discrete-Time Imprecise Markov Chains

摘要

Notably, even if an imprecise Markov chain is ergodic (and hence also weakly ergodic) and therefore both and exist, these inferences will not necessarily coincide. This was first observed in an experimental setting [ , Section 7.6], but the differences that were observed there were marginal. The following example shows that these differences can in fact be very substantial.