Aggregation of Markov flows I: theory

R. S. MacKay, J. D. Robinson
2018 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
A Markov flow is a stationary measure, with the associated flows and mean first passage times, for a continuous-time regular jump homogeneous semi-Markov process on a discrete state-space. Nodes in the state-space can be eliminated to produce a smaller Markov flow which is a factor of the original one. Some improvements to elimination methods of Wales are given. The main contribution of the paper is to present an alternative, namely a method to aggregate groups of nodes to produce a factor. The
more » ... oduce a factor. The method can be iterated to make hierarchical aggregation schemes. The potential benefits are efficient computation, including recomputation to take into account local changes, and insights into the macroscopic behaviour.
doi:10.1098/rsta.2017.0232 pmid:29555805 fatcat:x2w27o3yvjcelpkllbhygrsa2i