Asymptotic genealogy of a critical branching process

Annals of Applied Probability

Volumn 14, Issue 4, 2004, Pages 2120-2148

  Popovic, Lea ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Brownian excursion; Critical branching process; Galton Watson process; Genealogy; Point process; Random tree

Indexed keywords

EID: 26844542229     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051604000000486     Document Type: Article

References (20)

1. ABRAHAM, R. (1992). Un arbre aléatoire infini associé à l'excursion Brownienne. Séminaire de Probabilités XXVI. Lecture Notes in Math. 1526 374-397. Springer, New York.
2. ABRAHAM, R. and MAZLIAK, L. (1998). Branching properties of Brownian paths and trees. Exposition. Math. 16 59-74.
3. ALDOUS, D. (1993). The continuum random tree, III. Ann. Probab. 21 248-289.
4. ALDOUS, D. and POPOVIC, L. (2003). Coherent modeling of macroevolution. Preprint.
5. BILLINGSLEY, P. (1999). Convergence of Probability Measures, 3rd ed. Wiley, New York.
6. DURRETT, R. (1978). The genealogy of critical branching processes. Stochastic Process. Appl. 8101-116.
7. EWENS, W. J. (1979). Mathematical Population Genetics. Springer, New York.
8. FELLER, W. (1968). An Introduction to Probability Theory and Its Applications 1, 3rd ed. Wiley, New York.
9. GEIGER, J. (1995). Contour processes of random trees. In Stochastic Partial Differential Equations (A. Etheridge, ed.) 72-96. Cambridge Univ. Press.
10. HOBSON, D. G. (2000). Marked excursions and random trees. Séminaire de Probabilités XXXIV. Lecture Notes in Math. 1729 289-301. Springer, New York.
11. KINGMAN, J. F. C. (1980). Mathematics of Genetic Diversity. SIAM, Philadelphia.
12. LE GALL, J. F. (1989). Marches aléatoires, mouvement Brownien et processus de branchement. Séminaire de Probabilités XXIII. Lecture Notes in Math. 1372 258-274. Springer, New York.
13. LE GALL, J. F. (1991). Brownian excursions, trees and measure-valued branching processes. Ann. Probab. 19 1399-1439.
14. NEVEU, J. and PITMAN, J. W. (1989). Renewal property of the extrema and the tree property of a one-dimensional Brownian motion. Séminaire de Probabilités XXIII. Lecture Notes in Math. 1372 239-247. Springer, New York.
15. NEVEU, J. and PITMAN, J. W. (1989). The branching process in a Brownian excursion. Séminaire de Probabilités XXIII. Lecture Notes in Math. 1372 248-257. Springer, New York.
16. PITMAN, J. W. (2002). Combinatorial stochastic processes. Lecture notes for Saint-Flour course, July 2002. Technical Report SD-621, Univ. California, Berkeley.
17. POPOVIC, L. (2003). Asymptotic genealogy of a branching process and a model of macroevolution. Ph.D. dissertation, Univ. California, Berkeley.
18. REVUZ, D. and YOR, M. (1991). Continuous Martingales and Brownian Motion, 1st ed. Springer, New York.
19. ROGERS, L. C. G. and WILLIAMS, D. (1987). Diffusions, Markov Processes, and Martingales 1, 2, 2nd ed. Wiley, New York.
20. YULE, G. U. (1924). A mathematical theory of evolution, based on the conclusions of Dr J. C. Willis. Philos. Trans. Roy. Soc. London Ser. B 213 21-87.