This paper deals with discrete time Markov chain when the transition probabilities as well as the initial probabilities of a Markov chain may not be known precisely. The author discusses some modelling approaches which range from simple probability intervals to the general interval probability models and further to the models allowing completely general convex sets of probabilities. The basic idea is that precisely known initial distributions and transition matrices are replaced by imprecise ones, which effectively means that sets of possible candidates are considered. Consequently, sets of possible results are obtained and represented using similar imprecise probability models.
At first he sets up the model, then show how to perform calculations of the distributions corresponding to the consecutive steps of a Markov chain.
Next it is considered a generalisation of the concept of regularity and study the convergence of regular imprecise Markov chains.
Finally, the author gives some numerical examples.