On a two-color generalized Pólya urn

Metron

Volumn 63, Issue 1, 2005, Pages 115-134

  May, Caterina ^a   Paganoni, Anna Maria ^b   Secchi, Piercesare ^b  

^a UNIVERSITY OF MILAN   (Italy)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Asymptotic exchangeability; Generalized P lya urn; Random walks with reinforcement

Indexed keywords

EID: 35548947355     PISSN: 00261424     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Arthur, B., Ermol'ev, Y., and Kaniovskii, Y. (1983) A generalized urn problem and its applications, Cibernetics, 19, 61-71.
2. Athreya, K. B. and Karlin, S. (1968) Embedding of urn schemes into continuous time Markov branching processes and related limit theorems, Annals of Mathematical Statistics, 39(6), 1801-1817.
3. Athreya, K. B. (1969) On a characteristic property of Pólya's urn, Studia Scientiarum Mathematicarum Hungarica, 4, 31-35.
4. Bai, Z.D. and Hu, F. (1999) Asymptotic theorems for urn models with nonhomogeneus generating matrices, Stochastic Processes and Their Applications, 80, 87-101.
5. Berti, P., Pratelli, L., and Rigo, P. (2004) Limit theorems for a class of identically distributed random variables, Annals of Probability, 32(3A), 2029-2052.
6. Blackwell, D. and MacQueen, J. B. (1973) Ferguson distributions via Pólya urn schemes, Annals of Statistics, 1, 353-355.
7. Chow, Y.S. and Teicher, H. (1988) Probability Theory, 2nd edition, Springer-Verlag, New York.
8. Eggenberger, F. and Polya, G. (1923) Über die Statistik verketteter Vorgänge, Zeitschrift für Angewandte Mathemathik und Mechanik, 3, 279-289.
9. Dirienzo, A. G. (2000) Using urn models for the design of clinical trials, Sankhya, Series B, 62, no. 1, 43-69.
10. Freedman, D. (1965) Bernard Friedman's urn, Annals of Mathematical Statistics, 36, 956-970.
11. Friedman, B. (1949) A simple urn model, Communications on Pure and Applied Mathematics, 2, 59-70.
12. Higueras, I., Moler, J., Plo, F., and San Miguel, M. (2003) Urn models and differential algebraic equations, Journal of Applied Probability, 40, 401-412.
13. Hill, B. M., Lane, D., and Sudderth (1980) A strong law for some generalized urn processes, Annals of Probability, 8, 214-226.
14. Hill, B. M., Lane, D., and Sudderth (1987) Exchangeable urn processes, Annals of Probability, 15, 1592-1596.
15. Kingman, J. F. C. (1978) Uses of exchangeability, Annals of Probability, 6, no. 2, 183-197.
16. Kots, S., Mahmoud, H., and Robert, P. (2000) On generalized Pólya urn models, Statistics and Probability Letters, 49, 163-173.
17. Muliere, P., Paganoni, A. M., and Secchi, P. (2005) A randomly reinforced urn, to appear on Journal of Statistical Planning and Inference.
18. Paganoni, A. M. and Secchi, P. (2004) Interacting Reinforced Urn Systems, Advances in Applied Probability, 36(3), 791-804.
19. Pemantle, R. (1990) A time-dependent version of Pólya's urn, Jour. Theor. Prob., 3, 627-637.
20. Rosenberger, W. F. (1996) New directions in adaptive designs, Statistical Science, 11(2), 137-149.
21. Rosenberger, W. F. (2002) Randomized urn models and sequential design, Sequential Analysis, 21, 1-28.
22. Smythe, R. T. (1996) Central limit theorems for urn models, Stochastic Processes and Their Applications, 65, 115-137.