Average behaviour of imprecise Markov chains : a single pointwise ergodic theorem for six different models

We study the average behaviour of imprecise Markov chains; a generalised type of Markov chain where local probabilities are partially specified, and where structural assumptions such as Markovianity are weakened. In particular, we prove a pointwise ergodic theorem that provides (strictly) almost sure bounds on the long term average of any real function of the state of such an imprecise Markov chain. Compared to an earlier ergodic theorem by De Cooman et al. (2006), our result requires weaker conditions, provides tighter bounds, and applies to six different types of models.

Publication year:2021

Accessibility:Open