On Misapplications of Diffusion Approximations in Birth and Death Processes of Noisy Evolution

Kaniovski, Y.M. (1998). On Misapplications of Diffusion Approximations in Birth and Death Processes of Noisy Evolution. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-98-050

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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.

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