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First passage times and lumpability of semi-Markov processes
Ushio Sumita, Maria Rieders
Journal:

Journal of Applied Probability / Volume 25 / Issue 4 / December 1988

Published online by Cambridge University Press:

14 July 2016, pp. 675-687

Print publication:

December 1988
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A necessary and sufficient condition of Serfozo (1971) for lumpability of semi-Markov processes is reinterpreted in terms of first-exit times. Furthermore, a new necessary and sufficient condition is developed by establishing relationships between first-passage times and lumpability of semi-Markov processes. The approach taken in this paper is entirely based on the Laplace-transform domain.

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First passage times and lumpability of semi-Markov processes