Weak lumpability in finite Markov chains
Atef M. Abdel-moneim, Frederick W. Leysieffer · Journal of Applied Probability · 1982
Criteria are given to determine whether a given finite Markov chain can be lumped weakly with respect to a given partition of its state space. These conditions are given in terms of solution classes of systems of linear equations associated with the transition probability matrix of the Markov chain and the given partition.