Abstract

We are concerned with the equilibrium distribution of the th element in a sequence of continuous-time density-dependent Markov processes on the integers. Under a th moment condition on the jump distributions, we establish a bound of order on the difference between the point probabilities of and those of a translated Poisson distribution with the same variance. Except for the factor , the result is as good as could be obtained in the simpler setting of sums of independent, integer-valued random variables. Our arguments are based on the Stein-Chen method and coupling.