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Central limit theorems for multicolor urns with dominated colors

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  • Berti, Patrizia
  • Crimaldi, Irene
  • Pratelli, Luca
  • Rigo, Pietro

Abstract

An urn contains balls of d>=2 colors. At each time n>=1, a ball is drawn and then replaced together with a random number of balls of the same color. Let diag (An,1,...,An,d) be the n-th reinforce matrix. Assuming that EAn,j=EAn,1 for all n and j, a few central limit theorems (CLTs) are available for such urns. In real problems, however, it is more reasonable to assume that for some integer 1

Suggested Citation

  • Berti, Patrizia & Crimaldi, Irene & Pratelli, Luca & Rigo, Pietro, 2010. "Central limit theorems for multicolor urns with dominated colors," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1473-1491, August.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:8:p:1473-1491
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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.
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    1. Crimaldi, Irene & Dai Pra, Paolo & Minelli, Ida Germana, 2016. "Fluctuation theorems for synchronization of interacting Pólya’s urns," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 930-947.
    2. Crimaldi, Irene & Louis, Pierre-Yves & Minelli, Ida G., 2022. "An urn model with random multiple drawing and random addition," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 270-299.
    3. Sandra Fortini & Sonia Petrone & Hristo Sariev, 2021. "Predictive Constructions Based on Measure-Valued Pólya Urn Processes," Mathematics, MDPI, vol. 9(22), pages 1-19, November.

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