A comparison of diffusion approximations and actual limits in birth and death processes of noisy evolution

The stationary distribution of a birth and death process may not be approxi mated by a diffusion. The general situation is illustrated on the "musical chairs" model by Binmore et ai. (1995). This model is shown to generate outcomes which are not captured by the conc ept of the ultralong run equilibrium selection introduced in Binmore et al. (1995).