Limit behaviour of imprecise Markov chains: ergodicity versus weak ergodicity

This talk is concerned with the limit behaviour of imprecise Markov chains; a generalised type of Markov chain where the local dynamics are partially specified, and where structural assumptions such as Markovianity and/or time-homogeneity can be weakened. In particular, I will discuss how concepts and results concerning the limit behaviour of standard Markov chains can be generalized to this imprecise context. Most importantly, this includes the notion of ergodicity, the idea of a limit distribution, and the famous point-wise ergodic theorem. I will explain the various ways in which these things can be generalized, explore the similarities and differences with the classical setting, and argue why and when ergodicity should be replaced be the in my view more useful notion of weak ergodicity.