Imprecise Markov chains with absorption

We consider convergence of Markov chains with uncertain parameters, known as imprecise Markov chains, which contain an absorbing state. We prove that under conditioning on non-absorption the imprecise conditional probabilities converge independently of the initial imprecise probability distribution if some regularity conditions are assumed. This is a generalisation of a known result from the classical theory of Markov chains by Darroch and Seneta [6].