 Convergence of generalized urn models to non-equilibrium attractorsMathieu Faure () and Sebastian Schreiber Post-Print from HAL Abstract: Generalized Polya urn models have been used to model the establishment dynamics of a small founding population consisting of k di?erent genotypes or strategies. As population sizes get large, these population processes are well-approximated by a mean limit ordinary di?erential equation whose state space is the k simplex. We prove that if this mean limit ODE has an attractor at which the temporal averages of the population growth rate is positive, then there is a positive probability of the population not going extinct (i.e. growing without bound) and its distribution converging to the attractor. Conversely, when the temporal averages of the population growth rate is negative along this attractor, the population distribution does not converge to the attractor. For the stochastic analog of the replicator equations which can exhibit non-equilibrium dynamics, we show that verifying the conditions for convergence and non-convergence reduces to a simple algebraic problem. We also apply these results to selection-mutation dynamics to illustrate convergence to periodic solutions of these population genetics models with positive probability. Keywords: Economie; quantitative (search for similar items in EconPapers) Published in Stochastic Processes and their Applications, 2015, 125 (8), pp.3053--3074. ⟨10.1016/j.spa.2015.02.011⟩ There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01456122 DOI: 10.1016/j.spa.2015.02.011 Access Statistics for this paper More papers in Post-Print from HAL |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.