Article ID: | iaor1998354 |
Country: | United Kingdom |
Volume: | 29 |
Issue: | 1 |
Start Page Number: | 56 |
End Page Number: | 91 |
Publication Date: | Mar 1997 |
Journal: | Advances in Applied Probability |
Authors: | Ball Frank, Milne Robin K., Tame Ian D., Yeo Geoffrey F. |
Keywords: | quality & reliability |
Consider a system of interacting finite Markov chains in continuous time, where each subsystem is aggregated by a common partitioning of the state space. The interaction is assumed to arise from dependence of some of the transition rates for a given subsystem at a specified time on the states of the other subsystems at that time. With two subsystem classes, labelled 0 and 1, the superposition process arising from a system counts the number of subsystems in the latter class. Key structure and results from the theory of aggregated Markov processes are summarized. These are then applied also to superposition processes. In particular, we consider invariant distributions for the level