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2 results

  • Nonlinear and unbalanced urn models with two types of strategies: a stochastic approximation point of view

  • Soumaya Idriss
  • Journal:
    Probability in the Engineering and Informational Sciences / Volume 37 / Issue 3 / July 2023
    Published online by Cambridge University Press:
    20 May 2022, pp. 711-729
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  • In this paper, we treat a nonlinear and unbalanced $2$-color urn scheme, subjected to two different nonlinear drawing rules, depending on the color withdrawn. We prove a central limit theorem as well as a law of large numbers for the urn composition. We also give an estimate of the mean and variance of both types of balls.

  • A central limit theorem, and related results, for a two-color randomly reinforced urn

  • Part of
  • Giacomo Aletti, Caterina May, Piercesare Secchi
  • Journal:
    Advances in Applied Probability / Volume 41 / Issue 3 / September 2009
    Published online by Cambridge University Press:
    01 July 2016, pp. 829-844
    Print publication:
    September 2009
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  • We prove a central limit theorem for the sequence of random compositions of a two-color randomly reinforced urn. As a consequence, we are able to show that the distribution of the urn limit composition has no point masses.