On Misapplications of Diffusion Approximations in Birth and Death Processes of Noisy Evolution
Abstract
Birth and death processes with a finite number of states are used in modeling different kinds of noisy learning processes in economics. To analyze the long run properties one looks a the corresponding stationary distribution. When the number of states is large, the stationary distribution becomes bulky and difficult to analyze. To simplify the analysis in such a situation and hence to make the long run properties of the learning process more transparent, a diffusion approximation has been suggested. Unfortunately, quite often such such approximation is not correctly done. Why this happens and how the situation can be fixed is discussed in this note.