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Azuma-Hoeffding bounds for a class of urn models

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  • Dasgupta, Amites

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.

Suggested Citation

  • Dasgupta, Amites, 2024. "Azuma-Hoeffding bounds for a class of urn models," Statistics & Probability Letters, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:stapro:v:204:y:2024:i:c:s0167715223001645
    DOI: 10.1016/j.spl.2023.109940
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    References listed on IDEAS

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    1. Franchini, Simone, 2017. "Large deviations for generalized Polya urns with arbitrary urn function," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3372-3411.
    2. Grama, Ion & Haeusler, Erich, 2000. "Large deviations for martingales via Cramér's method," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 279-293, February.
    3. Janson, Svante, 2004. "Functional limit theorems for multitype branching processes and generalized Pólya urns," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 177-245, April.
    4. Smythe, R. T., 1996. "Central limit theorems for urn models," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 115-137, December.
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