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Nonlinear Unbalanced Urn Models via Stochastic Approximation

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  • Soumaya Idriss

    (University of Monastir)

Abstract

This paper presents a link between unbalanced non-linear urn model (a two-colored urn model) and stochastic approximation theory. Findings of our study reveal a successful establishment of limit laws for the urn composition, obtained under a drawing rule reinforced by an ℝ + $\mathbb {R}_{+}$ -valued concave function and a non-balanced replacement matrix.

Suggested Citation

  • Soumaya Idriss, 2022. "Nonlinear Unbalanced Urn Models via Stochastic Approximation," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 413-430, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09858-6
    DOI: 10.1007/s11009-021-09858-6
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    References listed on IDEAS

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    1. Bai, Z. D. & Hu, Feifang & Shen, Liang, 2002. "An Adaptive Design for Multi-Arm Clinical Trials," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 1-18, April.
    2. 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.
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