Azuma-Hoeffding bounds for a class of urn models

Amites Dasgupta

Statistics & Probability Letters, 2024, vol. 204, issue C

Abstract: We obtain Azuma-Hoeffding bounds, which are exponentially decreasing, for the probabilities of being away from the limit for a class of urn models. The method consists of relating the variables to certain linear combinations using eigenvectors of the replacement matrix, thus bringing in appropriate martingales. Some cases of repeated eigenvalues are also considered using cyclic vectors. Moreover, strong convergence of proportions is proved as an application of these bounds.

Keywords: Urn models; Martingales; Azuma inequality; Large deviation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2023.109940

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