论文信息 - Central limit theorems for multicolor urns with dominated colors

Central limit theorems for multicolor urns with dominated colors

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

[1] Luca Pratelli,et al. Limit theorems for a class of identically distributed random variables , 2004, math/0410105.

[2] Feifang Hu,et al. Asymptotics in randomized urn models , 2005 .

[3] Luca Pratelli,et al. A Strong Form of Stable Convergence , 2007 .

[4] N. Flournoy,et al. Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn , 2009, 0904.0350.

[5] Svante Janson,et al. Functional limit theorems for multitype branching processes and generalized Pólya urns , 2004 .

[6] A survey of random processes with reinforcement , 2007, math/0610076.

[7] C. C. Heyde,et al. Central Limit Theorem , 2006 .

[8] P. Hall,et al. Martingale Limit Theory and Its Application , 1980 .

[9] Anna Maria Paganoni,et al. A randomly reinforced urn , 2006 .

[10] Svante Janson,et al. Limit theorems for triangular urn schemes , 2006 .

[11] Luca Pratelli,et al. A Central Limit Theorem and its Applications to Multicolor Randomly Reinforced Urns , 2009, Journal of Applied Probability.

[12] P. Secchi,et al. A central limit theorem, and related results, for a two-color randomly reinforced urn , 2008, Advances in Applied Probability.

[13] Stanislav Volkov,et al. Vertex-reinforced random walk on Z has finite range , 1999 .