STRUCTURAL DECOMPOSITION OF MULTIPLE TIME SCALE "n,,- MARKOV PROCESSES"

A straightforward algorithm for the multiple time scale decomposition of singularly perturbed Markov processes has been presented.-fk2That algorithm provides a uniform approximation of the probability transition function over the interval t> 0 through the construction of a sequence of aggregate models valid at successively slower time scales. When only the structure of these models is desired, the algorithm can be expressed simply in terms of graphs associated with each of the aggregated models. The major computation then becomes computing shortest paths in these graphs. This representation of the algorithm furthermore allows analysis of more complex systems where there are multiple perturbation parameters with unknown relative orders of magnitude. * Keywords: Markov processes; singular perturbation; multiple time scales, graph theory.