Itô's excursion theory and random trees

Stochastic Processes and their Applications

Volumn 120, Issue 5, 2010, Pages 721-749

  Le Gall, Jean François ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

Brownian excursion; Galton Watson tree; It 's excursion theory; Random tree

Indexed keywords

ASYMPTOTIC BEHAVIORS; BROWNIAN EXCURSION; CONTOUR FUNCTIONS; GALTON-WATSON TREE; RANDOM TREE;

ASYMPTOTIC ANALYSIS; BROWNIAN MOVEMENT;

GRAPH THEORY;

EID: 77949489335     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2010.01.015     Document Type: Article

References (29)

1. Aldous D. The continuum random tree II: An overview. In: Barlow M.T., and Bingham N.H. (Eds). Stochastic Analysis (1991), Cambridge University Press, Cambridge 23-70
2. Aldous D. The continuum random tree III. Ann. Probab. 21 (1993) 248-289
3. Aldous D. Tree-based models for random distribution of mass. J. Stat. Phys. 73 (1993) 625-641
4. Athreya K.B., and Ney P.E. Branching Processes (1972), Springer, Berlin
5. Bertoin J. Lévy Processes (1996), Cambridge University Press, Cambridge
6. Biane P., and Yor M. Valeurs principales associées aux temps locaux browniens. Bull. Sci. Math. 111 (1987) 23-101
7. Burdzy K. Multidimensional Brownian Excursions and Potential Theory (1987), Longman, London
8. Chung K.L. Excursions in Brownian motion. Ark. Mat. 14 (1976) 155-177
9. Duquesne T., and Le Gall J.F. Random Trees, Lévy Processes and Spatial Branching Processes vol. 281 (2002), Astérisque
10. Ethier S.N., and Kurtz T. Markov Processes: Characterization and Convergence (1985), Wiley, New York
11. Evans S.N. Probability and Real Trees. Lecture Notes Math. vol. 1920 (2007), Springer, Berlin
12. Flajolet P., and Odlyzko A.M. The average height of binary trees and other simple trees. J. Comput. Syst. Sci. 25 (1982) 171-213
13. Geiger J., and Kersting G. The Galton-Watson tree conditioned on its height. Proceedings 7th Vilnius Conference on Probability and Mathematical Statistics (1999), VSP, Utrecht 277-286
14. K. Itô, Point processes and their applications to Markov processes, Lecture Notes Kyoto University, 1969.
15. K. Itô, Poisson point processes attached to Markov processes, in: Proceedings Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. III, University of California Press, Berkeley, 1972, pp. 225-239.
16. Kesten H., and Pittel B. A local limit theorem for the number of nodes, the height, and the number of final leaves in a critical branching process tree. Random Structures Algorithms 8 (1996) 243-299
17. Le Gall J.F. Brownian excursions, trees and measure-valued processes. Ann. Probab. 19 (1991) 1399-1439
18. Le Gall J.F. Spatial Branching Processes, Random Snakes and Partial Differential Equations (1999), Birkhäuser, Boston
19. Le Gall J.F. Random trees and applications. Probab. Surv. 2 (2005) 245-311
20. Lévy P. Processus Stochastiques et Mouvement Brownien (1948), Gauthier-Villars, Paris
21. Marckert J.F., and Mokkadem A. The depth first processes of Galton-Watson trees converge to the same Brownian excursion. Ann. Probab. 31 (2003) 1655-1678
22. Meyer P.A. Processus de Poisson ponctuels, d'après K. Itô. Séminaire de Probabilités V. Lecture Notes Math. vol. 191 (1971), Springer, Berlin
23. Pitman J. Combinatorial Stochastic Processes. Lecture Notes Math. vol. 1875 (2006), Springer, Berlin
24. Pitman J., and Yor M. Itô's excursion theory and its applications. Jpn. J. Math. 2 (2007) 83-96
25. Revuz D., and Yor M. Continuous Martingales and Brownian Motion (1992), Springer, Berlin
26. Roynette B., and Yor M. Penalizing Brownian Paths. Lecture Notes Math. vol. 1969 (2009), Springer, Berlin
27. Spitzer F. Principles of Random Walk (2001), Springer, Berlin
28. Stanley R.P. Enumerative Combinatorics, Vol. 2 (1999), Cambridge University Press, Cambridge
29. Watanabe S. Itô's theory of excursion point processes and its developments. Stochastic Process. Appl. 120 (2010) 653-677