A necessary condition for weak lumpability in finite Markov processes

James Ledoux (1)

1 INRIA Rennes

Under certain conditions, the state space of a homogeneous Markov process can be partitionned to construct an aggregated Markovian process. However, the verification of these conditions requires expensive computations. In this note, we expose a necessary condition for having a Markovian aggregated process. This conditions is based on properties of the eigenvalues of certain submatrices of the transition rate matrix of the original Markov process.

Domaines: Probabilités [math.PR]; Performance et fiabilité [cs.PF]; Recherche opérationnelle [math.OC]

James Ledoux. A necessary condition for weak lumpability in finite Markov processes. Operations Research Letters, 1993, 13 (3), pp.165-168. ⟨10.1016/0167-6377(93)90006-3⟩. ⟨hal-00852842⟩