Article ID: | iaor1999345 |
Country: | United Kingdom |
Volume: | 34 |
Issue: | 4 |
Start Page Number: | 847 |
End Page Number: | 858 |
Publication Date: | Dec 1997 |
Journal: | Journal of Applied Probability |
Authors: | Ledoux James |
We consider weak lumpability of finite homogeneous Markov chains, which is when a lumped Markov chain with respect to a partition of the initial state space is also a homogeneous Markov chain. We show that weak lumpability is equivalent to the existence of a direct sum of polyhedral cones that is positively invariant by the transition probability matrix of the original chain. It allows us, in a unified way, to derive new results on lumpability of reducible Markov chains and to obtain spectral properties associated with lumpability.