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Weak lumpability in finite Markov chains

  • Atef M. Abdel-moneim (a1) and Frederick W. Leysieffer (a1)

Abstract

Criteria are given to determine whether a given finite Markov chain can be lumped weakly with respect to a given partition of its state space. These conditions are given in terms of solution classes of systems of linear equations associated with the transition probability matrix of the Markov chain and the given partition.

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Corresponding author

Postal address: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, FL 32306, U.S.A.

References

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[1] Burke, C. J. and Rosenblatt, M. (1958) A Markovian function of a finite Markov chain. Ann. Math. Statist. 29, 11121122.
[2] Hachigian, J. and Rosenblatt, M. (1963) Collapsed Markov chains and the Chapman–Kolmogorov equation. Ann. Math. Statist. 34, 233237.
[3] Kemeny, J. G. and Snell, J. L. (1978) Finite Markov Chains, 2nd edn. Springer-Verlag, New York.

Keywords

Weak lumpability in finite Markov chains

  • Atef M. Abdel-moneim (a1) and Frederick W. Leysieffer (a1)

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