A recent result of Fourneau et. al. derives conditions under which the joint state of a set of Markov chains with functional rates has a product-form solution for its equilibrium state probabilities, when they exist. The present note shows how the Reversed Compound Agent Theorem (RCAT) obtains the same result in a few lines. In fact a more general result also follows.
Information from pubs.doc.ic.ac.uk/frcat.