AGGREGATION OF MARKOV-CHAINS

For a collection of Markov chains the aggregated process, that is a process for which the transition rates are a mixture of the transition rates of the Markov chains in the collection, is introduced. A sufficient condition is given, called cross-balance, a generalization of global balance to a collection of processes, under which the equilibrium distribution of the aggregated process is shown to be the same mixture of the equilibrium distributions of the Markov chains in the collection. A number of examples are discussed including a construction method for constructing the equilibrium distribution.