Large deviations for Dirichlet processes and Poisson-Dirichlet distribution with two parameters

Electronic Journal of Probability

Volumn 12, Issue , 2007, Pages 787-807

  Feng, Shui ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Dirichlet processes; Gem representation; Large deviation principles; Poisson Dirichlet distribution; Two parameter Poisson Dirichlet distribution

Indexed keywords

EID: 34249910056     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v12-417     Document Type: Article

References (23)

1. M. Aoki (2006). Thermodynamic limit of macroeconomic or financial models: one- and two-parameter Poisson-Dirichlet models. Preprint.
2. M.A. Carlton (1999). Applications of the two-parameter Poisson-Dirichlet distribution. Unpublished Ph.D. thesis, Dept. of Statistics, University of California, Los Angeles.
3. D. Dawson and S. Feng (2001). Large deviations for the Fleming-Viot process with neutral mutation and selection, II. Stock. Proc. Appl. 92, 131-162.
4. D. Dawson and S. Feng (2006). Asymptotic behavior of Poisson-Dirichlet distribution for large mutation rate. Ann. Appl. Probab., Vol.16, No. 2, 562-582.
5. A. Dembo and O. Zeitouni. Large deviations techniques and applications. Second edition. Applications of Mathematics, 38. Springer-Verlag, New York, 1998.
6. B. Derrida (1997). From random walks to spin glasses. Pkysica D, 107, 186-198.
7. W.J. Ewens. Mathematical Population Genetics, Vol. I. Springer-Verlag, New York, 2004.
8. S. Feng and F.M. Hoppe (1998). Large deviation principles for some random combinatorial structures in population genetics and Brownian motion. Ann. Appl. Probab., Vol. 8, No. 4, 975-994.
9. T.S. Ferguson (1973). A Baysian analysis of some nonparametric problems. Ann. Stat., 1:209-230.
10. R.A. Fisher, A.S. Corbet and C.B. Williams (1943). The relation between the number of species and the number of individuals in a random sample of an animal population. J. Animal Ecology, 12:42-58.
11. J.H. Gillespie (1999). The role of population size in molecular evolution. Theoretical Population Biology, 55 145-156.
12. F.M. Hoppe (1984). Polya-like urns and the Ewens sampling formula. Journal of Mathematical Biology, 20, 91-94.
13. P. Joyce, S.M. Krone, and T.G. Kurtz (2003). When can one detect overdominant selection in the infinite-alleles model? Ann. Appl. Probab., 13, No. 1, 181-212.
14. J.C.F. Kingman (1975). Random discrete distributions. J. Roy. Statist. Soc. B, 37, 1-22.
15. Lynch, J. and Sethuraman, J. (1987). Large deviations for processes with independent increments. Ann. Probab., 15:610-627.
16. M. Perman (1993). Order statistics for jumps of normalised subordinators. Stoch. Proc. Appl., 46, 267-281.
17. J. Pitman (1996). Random discrete distributions invariant under size-biased permutation. Adv. Appl. Probab., 28, 525-539.
18. J. Pitman (1995). Exchangeable and partially exchangeable random partitions. Prob. Theory Rel. Fields, 102, 145-158.
19. J. Pitman (1996). Some developments of the Blackwell-MacQueen urn scheme. In Statistics, Probability and Game Theory. Papers in Honor of David Blackwell (T.S. Ferguson, L.S. Shapley, and J.B. MacQueen, eds.), 245-267. IMS Lecture Notes-Monograph series, Vol. 30.
20. J. Pitman and M. Yor (1997). The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab.,Vol. 25, No. 2, 855-900.
21. A.A. Puhalskii. On functional principle of large deviations. In V.Sazonov and T. Sher-vashidze, editors. New Trends in Probability and Statistics. pages 198-218. VSP Moks'las, Moskva, 1991.
22. L.A. Shepp and S.P. Lloyd (1966). Ordered cycle length in a random permutation. Trans. Amer. Math. Soc. Probab.,Vol. 121, 340-357.
23. A.M. Vershik (1986). The asymptotic distribution of factorizations of natural numbers into prime divisors. Soviet Math. Dokl., 34:57-61.