IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v127y2017i10p3372-3411.html
   My bibliography  Save this article

Large deviations for generalized Polya urns with arbitrary urn function

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915300314
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2017.02.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Kotz, Samuel & Mahmoud, Hosam & Robert, Philippe, 2000. "On generalized Pólya urn models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 163-173, August.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Narduzzo, Alessandro & Warglien, Massimo, 1996. "Learning from the Experience of Others: An Experiment on Information Contagion," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 5(1), pages 113-126.
    2. Jean-Michel Dalle, 1995. "Dynamiques d'adoption, coordination et diversité : la diffusion des standards technologiques," Revue Économique, Programme National Persée, vol. 46(4), pages 1081-1098.
    3. Giulio Bottazzi & Ugo M. Gragnolati & Fabio Vanni, 2017. "Non-linear externalities in firm localization," Regional Studies, Taylor & Francis Journals, vol. 51(8), pages 1138-1150, August.
    4. Fontanelli, Luca & Guerini, Mattia & Napoletano, Mauro, 2023. "International trade and technological competition in markets with dynamic increasing returns," Journal of Economic Dynamics and Control, Elsevier, vol. 149(C).
    5. Luigi Marengo & Paolo Zeppini, 2016. "The arrival of the new," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 171-194, March.
    6. Tatsuhiro Shichijo & Emiko Fukuda, 2019. "A dynamic game analysis of Internet services with network externalities," Theory and Decision, Springer, vol. 86(3), pages 361-388, May.
    7. Heinrich, Torsten, 2016. "The Narrow and the Broad Approach to Evolutionary Modeling in Economics," MPRA Paper 75797, University Library of Munich, Germany.
    8. M. Keilbach & M. Posch, 1998. "Network Externalities and the Dynamics of Markets," Working Papers ir98089, International Institute for Applied Systems Analysis.
    9. Egidi, Massimo & Narduzzo, Alessandro, 1997. "The emergence of path-dependent behaviors in cooperative contexts," International Journal of Industrial Organization, Elsevier, vol. 15(6), pages 677-709, October.
    10. Dosi, Giovanni & Nelson, Richard R., 2010. "Technical Change and Industrial Dynamics as Evolutionary Processes," Handbook of the Economics of Innovation, in: Bronwyn H. Hall & Nathan Rosenberg (ed.), Handbook of the Economics of Innovation, edition 1, volume 1, chapter 0, pages 51-127, Elsevier.
    11. Max Keilbach, 1999. "Network Externalities and the Path Dependence of Markets: Will Bill Gates Make It?," Computing in Economics and Finance 1999 711, Society for Computational Economics.
    12. repec:ebl:ecbull:v:3:y:2005:i:45:p:1-14 is not listed on IDEAS
    13. Giorgio Fagiolo, 2005. "A Note on Equilibrium Selection in Polya-Urn Coordination Games," Economics Bulletin, AccessEcon, vol. 3(45), pages 1-14.
    14. Karolina Safarzyńska & Jeroen Bergh, 2010. "Evolutionary models in economics: a survey of methods and building blocks," Journal of Evolutionary Economics, Springer, vol. 20(3), pages 329-373, June.
    15. Ugo M. Gragnolati & Alessandro Nuvolari, 2023. "Innovation, localized externalities, and the British Industrial Revolution, 1700-1850," LEM Papers Series 2023/26, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    16. Flåm, Sjur Didrik & Gaasland, Ivar & Vårdal, Erling, 2006. "On Stabilizing or Deregulating Food Prices," Working Papers in Economics 08/06, University of Bergen, Department of Economics.
    17. Giovanni Dosi & Alessio Moneta & Elena Stepanova, 2019. "Dynamic increasing returns and innovation diffusion: bringing Polya Urn processes to the empirical data," Industry and Innovation, Taylor & Francis Journals, vol. 26(4), pages 461-478, April.
    18. Paolo Zeppini & Koen Frenken & Roland Kupers, 2013. "Threshold models of technological transitions," Working Papers 13-06, Eindhoven Center for Innovation Studies, revised Aug 2013.
    19. Heinrich, Torsten, 2014. "Standard wars, tied standards, and network externality induced path dependence in the ICT sector," Technological Forecasting and Social Change, Elsevier, vol. 81(C), pages 309-320.
    20. Jonathan H. Reed, 2022. "Operational and strategic change during temporary turbulence: evidence from the COVID-19 pandemic," Operations Management Research, Springer, vol. 15(1), pages 589-608, June.
    21. Mercure, Jean-François, 2018. "Fashion, fads and the popularity of choices: Micro-foundations for diffusion consumer theory," Structural Change and Economic Dynamics, Elsevier, vol. 46(C), pages 194-207.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:127:y:2017:i:10:p:3372-3411. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.