References
- Athreya, K., and S. Karlin. 1968. Embedding of urn schemes into continuous time Markov branching processes and related limit theorems. The Annals of Mathematical Statistics 39 (6):1801–1817.
- Athreya, K., and P. Ney. 1972. Branching process. New York: Springer-Verlag.
- Bagchi, A., and A. Pal. 1985. Asymptotic normality in the generalized Pólya-Eggenberger urn model with applications to computer data structures. SIAM Journal on Algebraic Discrete Methods 6 (3):394–405.
- Balaji, S., and H. Mahmoud. 2006. Exact and limiting distributions in diagonal pólya processes. Annals of the Institute of Statistical Mathematics 58 (1):171–185.
- Balaji, S., H. Mahmoud, and O. Watanabe. 2006. Distributions in the Ehrenfest process. Statistics & Probability Letters 76 (7):666–674.
- Chauvin, B., N. Pouyanne, and R. Sahnoun. 2011. Limit distributions for large pólya urns. The Annals of Applied Probability 21 (1):1–32.
- Chen, C., and H. Mahmoud. 2018. The continuous-time triangular process. Annals of the Institute of Statistical Mathematics 70 (2):303–321.
- Edwards, C., and D. Penney. 2007. Elementary differential equations. Upper Saddle River, NJ: Pearson Prentice Hall.
- Eggenberger, F., and G. Pólya. 1923. Über die statistik verketteter vorgänge. Zamm - Zeitschrift Für Angewandte Mathematik Und Mechanik 3 (4):279–289.
- Ehrenfest, P., and T. Ehrenfest. 1907. Über zwei bekannte einwände gegen das Boltzmannsche H-theorem. Physikalische Zeitschrift 8:311–314.
- Friedman, B. 1949. A simple urn model. Communications on Pure and Applied Mathematics 2 (1):59–70.
- Janson, S. 2004. Functional limit theorems for multitype branching processes and generalized pólya urns. Stochastic Processes and Their Applications 110 (2):177–245.
- Johnson, N., and S. Kotz. 1977. Urn models and their application. An approach to modern discrete probability theory. New York: John Wiley & Sons.
- Mahmoud, H. 2009. Pólya urn models. Boca Raton, FL: CRC Press.
- Rosenberger, W. 1996. New directions in adaptive designs. Statistical Science 11 (2):137–149.
- Sparks, J., and H. Mahmoud. 2013. Phases in the two-color tenable zero-balanced pólya processes. Statistics & Probability Letters 83 (1):265–271.
- Terwilliger, P. 2008. Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials. ArXiv: math.QA, math/0408390.
- Wei, L.-Y. 1979. The generalized pólya’s urn design for sequential medical trials. The Annals of Statistics 7 (2):291–296.
- Wei, L.-Y., and S. Durham. 1978. The randomized play-the-winner rule in medical trials. Journal of the American Statistical Association 73 (364):840–843.