In Markov chain theory a stochastic matrix $P$ is regular if some matrix power $P^n$ contains only strictly positive elements. Regularity of transition matrix of a Markov chain guarantees the existence of a unique invariant distribution which is also the limiting distribution. In the present paper a similar result is shown for the generalized Markov chain model that replaces classical probabilities with interval probabilities. We generalize the concept of regularity and show that for a regular interval transition matrix sets of probabilities corresponding to consecutive steps of a Markov chain converge to a unique limiting set of distributions that only depends on transition matrix and is independent of the initial distribution. A similar convergence result is also shown for approximations of the invariant set.
Keywords. Markov chains, interval probabilities
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Kardeljeva ploscad 5