A necessary condition for weak lumpability in finite Markov processes
نویسنده
چکیده
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 condition is based on properties of the eigenvalues of certain submatrices of the transition rate matrix of the original Markov process. Subject classification: Probability: Markov processes, Markov chains, Lumpability. ∗This work was partially supported by the grant 290C2010031305061 of the French Region Bretagne. 1
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تاریخ انتشار 1992