| Article ID: | iaor1989370 |
| Country: | United Kingdom |
| Volume: | 25 |
| Issue: | 4 |
| Start Page Number: | 675 |
| End Page Number: | 687 |
| Publication Date: | Dec 1988 |
| Journal: | Journal of Applied Probability |
| Authors: | Sumita Ushio, Rieders Maria |
A necessary and sufficient condition of Serfozo 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.