A necessary condition for weak lumpability in finite Markov processes

  • Authors:

  • James Ledoux

  • Affiliations:

  • IRISA-INRIA, Campus de Beaulieu, F-35042 Rennes Cedex, France

  • Venue:
  • Operations Research Letters
  • Year:
  • 1993

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Abstract

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.