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Large deviations for generalized Polya urns with arbitrary urn function

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  • Franchini, Simone

Abstract

We consider a generalized two-color Polya urn (black and white balls) first introduced by Hill et al. (1980), where the urn composition evolves as follows: let π:0,1→0,1, and denote by xn the fraction of black balls after step n, then at step n+1 a black ball is added with probability πxn and a white ball is added with probability 1−πxn. Originally introduced to mimic attachment under imperfect information, this model has found applications in many fields, ranging from Market Share modeling to polymer physics and biology.

Suggested Citation

  • Franchini, Simone, 2017. "Large deviations for generalized Polya urns with arbitrary urn function," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3372-3411.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:10:p:3372-3411
    DOI: 10.1016/j.spa.2017.02.010
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    References listed on IDEAS

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    1. Kotz, Samuel & Mahmoud, Hosam & Robert, Philippe, 2000. "On generalized Pólya urn models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 163-173, August.
    2. Brian Arthur, W. & Ermoliev, Yu. M. & Kaniovski, Yu. M., 1987. "Path-dependent processes and the emergence of macro-structure," European Journal of Operational Research, Elsevier, vol. 30(3), pages 294-303, June.
    3. Dosi, Giovanni & Ermoliev, Yuri & Kaniovski, Yuri, 1994. "Generalized urn schemes and technological dynamics," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 1-19, January.
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    Cited by:

    1. Dasgupta, Amites, 2024. "Azuma-Hoeffding bounds for a class of urn models," Statistics & Probability Letters, Elsevier, vol. 204(C).

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