  In this note we consider a Markov chain formed by a finite system of
interacting birth-and-death processes on a finite state space. We study an
asymptotic behaviour of the Markov chain as its state space becomes large. In
particular, we show that the appropriately scaled Markov chain converges to a
diffusion process, and derive conditions for existence of the stationary
distribution of the limit diffusion process in special cases.
