On generalized Pólya urn models

Statistics and Probability Letters

Volumn 49, Issue 2, 2000, Pages 163-173

  Kotz, Samuel ^a   Mahmoud, Hosam ^b   Robert, Philippe ^c  

^a George Washington University   (United States)

^b GEORGE WASHINGTON UNIVERSITY   (United States)

^c INRIA ROCQUENCOURT   (France)

Author keywords

05A05; 60C05; Discrete distributions; Stochastic differential equations; Urns

Indexed keywords

EID: 0042123091     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(00)00045-6     Document Type: Article

References (17)

1. Athreya K., Karlin S. Embedding of urn schemes into continuous time Markov branching process and related limit theorem. Ann. Math. Statist. 39:1968;1801-1817.
2. Athreya K., Ney P. Branching Processes. 1972;Springer, New York.
3. Bagchi A., Pal A. Asymptotic normality in the generalized Pólya-Eggenberger urn model with applications to computer data structures. SIAM J. Algebraic Discrete Methods. 6:1985;394-405.
4. Bernstein S. Sur un problème du schéma des urnes à composition variable. C. R. (Dokl.) Acad. Sci. URSS. 28:1940;5-7.
5. Eggenberger F., Pólya G. Über die Statistik verketetter Vorgäge. Z. Angew. Math. Mech. 1:1923;279-289.
6. Freedman D. Bernard Friedman's urn. Ann. Math. Statist. 36:1965;956-970.
7. Friedman B. A simple urn model. Comm. Pure Appl. Math. 2:1949;59-70.
8. Gouet R. A martingale approach to strong convergence in a generalized Pólya-Eggenberger urn model. Statist. Probab. Lett. 8:1989;225-228.
9. Gouet R. Martingale functional central limit theorems for a generalized Pólya Urn. Ann. Probab. 21:1993;1624-1639.
10. Jackson, J., (Circa) 1999. Some extensions and applications of Kriz' (1972) urn model. Ph.D. Dissertation, University of North Carolina.
11. Johnson N., Kotz S. Urn Models and their Applications. 1977;Wiley, New York.
12. Kriz J. Die PMP-verteilung. Statist. Hefte. 13:1972;211-224.
13. Pemantle R. Nonconvergence to unstable points in urn models and stochastic approximations. Ann. Probab. 18:1990;698-712.
14. Savkevich V. Sur le schéma des urnes à composition variable. C. R. (Dokl.) Acad. Sci. URSS. 28:1940;8-12.
15. Smythe R. Central limit theorems for urn models. Stochastic Process. Appl. 65:1996;115-137.
16. Rogers L., Williams D. Diffusions, Markov Processes and Martingales, Vol 2: Itô calculus. 1987;Wiley, New York.
17. Rosenblatt A. Sur le concept de contagion de M. G. Pólya dans le calcul des probabilités. Proc. Acad. Nac. Cien. Exactas, Fis. Nat., Peru (Lima). 3:1940;186-204.