Finite Discrete Time Markov Chains with Interval Probabilities

Abstract

A Markov chain model in generalised settings of interval probabilities is presented. Instead of the usual assumption of constant transitional probability matrix, we assume that at each step a transitional matrix is chosen from a set of matrices that corresponds to a structure of an interval probability matrix. We set up the model and show how to obtain intervals corresponding to sets of distributions at consecutive steps. We also state the problem of invariant distributions and examine possible approaches to their estimation in terms of convex sets of distributions, and in a special case in terms of interval probabilities.