EXACT AGGREGATION OF ABSORBING MARKOV-PROCESSES USING THE QUASI-STATIONARY DISTRIBUTION

We characterize the conditions under which an absorbing Markovian fini te process (in discrete or continuous time) can be transformed into a new aggregated process conserving the Markovian property, whose states are elements of a given partition of the original state space. To obt ain this characterization, a key tool is the quasi-stationary distribu tion associated with absorbing processes. It allows the absorbing case to be related to the irreducible one. We are able to calculate the se t of all initial distributions of the starting process leading to an a ggregated homogeneous Markov process by means of a finite algorithm. F inally, it is shown that the continuous-time case can always be reduce d to the discrete one using the uniformization technique.