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Central and Functional Central Limit Theorems for a Class of Urn Models

Author

Listed:
  • Gopal K. Basak

    (University of Bristol)

  • Amites Dasgupta

    (Stat-Math Unit, Indian Statistical Institute)

Abstract

We consider an approach based on tails to certain central limit and functional central limit theorems for a class of two color urn models. In particular, some of the results are derived from an associated Ornstein–Uhlenbeck process, and for another result we give an alternative proof based on martingale tails.

Suggested Citation

  • Gopal K. Basak & Amites Dasgupta, 2006. "Central and Functional Central Limit Theorems for a Class of Urn Models," Journal of Theoretical Probability, Springer, vol. 19(3), pages 741-756, December.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:3:d:10.1007_s10959-006-0048-8
    DOI: 10.1007/s10959-006-0048-8
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    References listed on IDEAS

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    1. 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.
    2. Gouet, Raúl, 1989. "A martingale approach to strong convergence in a generalized Pólya-Eggenberger urn model," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 225-228, August.
    3. Smythe, R. T., 1996. "Central limit theorems for urn models," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 115-137, December.
    4. Basak, Gopal K. & Hu, Inchi & Wei, Ching-Zong, 1997. "Weak convergence of recursions," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 65-82, May.
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