Coalescents with simultaneous multiple collisions

Electronic Journal of Probability

Volumn 5, Issue , 2000, Pages 1-50

  Schweinsberg, Jason ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Ancestral processes; Coalescence; Exchangeable; Markov processes; Poisson point processes; Random partitions

Indexed keywords

EID: 0001885968     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v5-68     Document Type: Article

References (19)

1. D. J. Aldous. Exchangeability and related topics. In P. L. Hennequin, editor, École d’Été de Probabilités de Saint-Flour XIII, Lecture Notes in Mathematics, Vol. 1117. Springer-Verlag, 1985.
2. J. Bertoin. Levy Processes. Cambridge University Press, 1996.
3. E. Bolthausen and A.-S. Sznitman. On Ruelle’s probability cascades and an abstract cavity method. Comm. Math. Phys., 197(2):247-276, 1998.
4. J. L. Doob. Measure Theory. Springer-Verlag, New York, 1994.
5. R. Durrett. Probability: Theory and Examples. 2nd ed. Duxbury Press, Belmont, CA, 1996.
6. S. N. Ethier and T. G. Kurtz. Markov Processes: Characterization and Convergence. Wiley, New York, 1986.
7. B. Fristedt and L. Gray. A Modern Approach to Probability Theory. Birkhauser, Boston, 1997.
8. N. L. Johnson and S. Kotz. Discrete Distributions. Wiley, New York, 1969.
9. J. F. C. Kingman. The representation of partition structures. J. London Math. Soc., 18:374-380, 1978.
10. J. F. C. Kingman. The coalescent. Stoch. Proc. Appl., 13: 235-248, 1982.
11. J. F. C. Kingman. On the genealogy of large populations. In J. Gani and E. J. Hannan, editors, Essays in Statistical Science, Papers in honour of P. A. P. Moran. J. Appl. Prob. Special Volume 19A, 27-43, 1982.
12. M. Möhle and S. Sagitov. A characterization of ancestral limit processes arising in haploid population genetics models. Berichte zur Stochastik und verwandten Gebieten, Johannes Gutenberg-Universitat Mainz, 1999.
13. M. Mohle and S. Sagitov. A classification of coalescent processes for haploid exchangeable population models. Available via http://www.math.chalmers.se/∼serik/coal.html, 1999.
14. M. Mohle and S. Sagitov. Coalescent patterns in exchangeable diploid population models. Berichte zur Stochastik und verwandten Gebieten, Johannes Gutenberg-Universitöt Mainz, 1999.
15. J. Pitman. Exchangeable and partially exchangeable random partitions. Probab. Theory Related Fields, 102:145-158, 1995.
16. J. Pitman. Coalescents with multiple collisions. Ann. Probab., 27:1870-1902, 1999.
17. D. Revuz and M. Yor. Continuous Martingales and Brownian Motion. 3rd ed. Springer-Verlag, Berlin, 1999.
18. S. Sagitov. The general coalescent with asynchronous mergers of ancestral lines. J. Appl. Probab., 36: 1116-1125, 1999.
19. J. Schweinsberg. A necessary and sufficient condition for the A-coalescent to come down from infinity. Electron. Comm. Probab., 5:1-11, 2000.