Negatively Reinforced Balanced Urn Schemes

Gursharn Kaur

doi:10.1016/2019.01.001

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arXiv · 1808.00796

Negatively Reinforced Balanced Urn Schemes

Gursharn Kaur

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Abstract

We consider weighted negatively reinforced urn schemes with finitely many colours. An urn scheme is called negatively reinforced, if the selection probability for a colour is proportional to the weight $w$ of the colour proportion, where $w$ is a non-increasing function. Under certain assumptions on the replacement matrix $R$ and weight function $w$, such as, $w$ is differentiable and $w(0) < \infty$, we obtain almost sure convergence of the random configuration of the urn model. In particular, we show that if $R$ is doubly stochastic the random configuration of the urn converges to the uniform vector, and asymptotic normality holds, if the number of colours in the urn are sufficiently large.

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Gursharn Kaur. 2018-08-02. Negatively Reinforced Balanced Urn Schemes. https://doi.org/10.1016/2019.01.001

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