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Interacting generalized Friedman’s urn systems

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  • Aletti, Giacomo
  • Ghiglietti, Andrea

Abstract

We consider systems of interacting Generalized Friedman’s Urns (GFUs) having irreducible mean replacement matrices. The interaction is modeled through the probability to sample the colors from each urn, that is defined as convex combination of the urn proportions in the system. From the weights of these combinations we individuate subsystems of urns evolving with different behaviors. We provide a complete description of the asymptotic properties of urn proportions in each subsystem by establishing limiting proportions, convergence rates and Central Limit Theorems. The main proofs are based on a detailed eigenanalysis and stochastic approximation techniques.

Suggested Citation

  • Aletti, Giacomo & Ghiglietti, Andrea, 2017. "Interacting generalized Friedman’s urn systems," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2650-2678.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:8:p:2650-2678
    DOI: 10.1016/j.spa.2016.12.003
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    References listed on IDEAS

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    1. Bai, Z. D. & Hu, Feifang, 1999. "Asymptotic theorems for urn models with nonhomogeneous generating matrices," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 87-101, March.
    2. Crimaldi, Irene & Dai Pra, Paolo & Minelli, Ida Germana, 2016. "Fluctuation theorems for synchronization of interacting Pólya’s urns," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 930-947.
    3. Smythe, R. T., 1996. "Central limit theorems for urn models," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 115-137, December.
    4. M. Marsili & A. Valleriani, 1998. "Self organization of interacting polya urns," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(4), pages 417-420, June.
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    Cited by:

    1. Aletti, Giacomo & Crimaldi, Irene & Ghiglietti, Andrea, 2024. "Networks of reinforced stochastic processes: Probability of asymptotic polarization and related general results," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    2. Crimaldi, Irene & Dai Pra, Paolo & Louis, Pierre-Yves & Minelli, Ida G., 2019. "Synchronization and functional central limit theorems for interacting reinforced random walks," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 70-101.
    3. Irene Crimaldi & Pierre-Yves Louis & Ida Minelli, 2020. "Interacting non-linear reinforced stochastic processes: Synchronization and no-synchronization," Working Papers hal-02910341, HAL.

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