Quick aggregation of Markov chain functionals via stochastic complementation

The paper presents a quick and simplified aggregation method for a large class of Markov chain functionals based on the concept of stochastic complementation. Aggregation results in a reduction in the number of Markov states by grouping them into a smaller number of aggregated states, thereby producing a considerable saving on computational complexity associated with maximum likelihood parameter and state estimation for hidden Markov models. The importance of the proposed aggregation method stems from the ease with which Markov chains with a large number of states can be aggregated. Three Markov chain functionals which have widespread use are considered to illustrate the application of our aggregation method.