Technical Note—An Eigenvector Condition for Markov Chain Lumpability

D. R. Barr and M. U. Thomas
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D. R. Barr: Naval Postgraduate School, Monterey, California
M. U. Thomas: Naval Postgraduate School, Monterey, California

Operations Research, 1977, vol. 25, issue 6, 1028-1031

Abstract: Under certain conditions the state space of a discrete parameter Markov chain may be partitioned to form a smaller “lumped” chain that retains the Markov property. Existing statements of conditions on the transition matrix P of the original chain characterizing such lumpability are difficult to verify in practice, especially when the dimension of P is large. An alternate approach, based on the eigenvectors of P , is presented and illustrated with examples.

Date: 1977
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