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

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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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  • Y.M. Kaniovski, 1998. "On Misapplications of Diffusion Approximations in Birth and Death Processes of Noisy Evolution," Working Papers ir98050, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:ir98050
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    1. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October.
    2. Binmore, K. & Samuelson, L. & Vaughan, R., 1993. "Musical Chairs: Modelling Noisy Evolution," Working papers 9324, Wisconsin Madison - Social Systems.
    3. Y.M. Kaniovski & G.C. Pflug, 1997. "Limit Theorems for Stationary Distributions of Birth-and-Death Processes," Working Papers ir97041, International Institute for Applied Systems Analysis.
    4. Orlean, Andre, 1995. "Bayesian interactions and collective dynamics of opinion: Herd behavior and mimetic contagion," Journal of Economic Behavior & Organization, Elsevier, vol. 28(2), pages 257-274, October.
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