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

Published online by Cambridge University Press:  20 May 2022

Soumaya Idriss Open the ORCID record for Soumaya Idriss [Opens in a new window]
Soumaya Idriss*
Affiliation:
University of Monastir, Monastir, Tunisia. E-mail: idriss.soumaya@gmail.com
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Abstract

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and unbalanced $2$-color urn scheme, subjected to two different nonlinear drawing rules, depending on the color withdrawn.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.

Keywords

Discrete-time martingalesLimit theoremsReinforced processesStochastic approximation theoryUrn models
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 3 , July 2023 , pp. 711 - 729
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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