On the theory of Markov set-chains

Abstract

In the theory of homogeneous Markov chains, states are classified according to their connectivity to other states and this classification leads to a classification of the Markov chains themselves. In this paper we classify Markov set-chains analogously, particularly into ergodic, regular, and absorbing Markov set-chains. A weak law of large numbers is developed for regular Markov set-chains. Examples are used to illustrate analysis of behavior of Markov set-chains.