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A comparison of diffusion approximations and actual limits in birth and death processes of noisy evolution |
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| Authors: | Yuri M. Kaniovski |
| Affiliation: | (1) School of Economics, Free University of Bozen, Bolzano, Via Sernesi 1, 39100 Bolzano, Italy (e-mail: Yuriy.Kaniovskyi@unibz.it), IT;(2) Department of Management and Computer Science (DISA), University of Trento, Via Inama 5, 38100 Trento, Italy (e-mail: kaniov@cs.unitn.it), IT |
| Abstract: | The stationary distribution of a birth and death process may not be approximated by a diffusion. The general situation is illustrated on the “musical chairs” model by Binmore et al. (1995). This model is shown to generate outcomes which are not captured by the concept of the ultralong run equilibrium selection introduced in Binmore et al. (1995). |
| Keywords: | :Birth and death process – Diffusion approximation – Learning – Equilibrium selection – Stationary distribution – Limit Gibbs potential |
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