Fragmentation at height associated with Lévy processes

Stochastic Processes and their Applications

Volumn 117, Issue 3, 2007, Pages 297-311

  Delmas, Jean François ^a  

^a UNIVERSITÉ PARIS EST   (France)

Author keywords

Continuous random tree; Dislocation measure; Fragmentation; L vy snake; Local time

Indexed keywords

ASYMPTOTIC STABILITY; MATHEMATICAL MODELS; PROBABILITY; TREES (MATHEMATICS);

CONTINUOUS RANDOM TREE; DISLOCATION MEASURES; FRAGMENTATION; LÉVY SNAKE; LOCAL TIME;

RANDOM PROCESSES;

EID: 33846465823     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2006.06.001     Document Type: Article

References (17)

1. R. Abraham, J.-F. Delmas, Fragmentation associated to Lávy processes, preprint CERMICS, 2005
2. R. Abraham, J.-F. Delmas, Asymptotics for the small fragments of the fragmentation at nodes, preprint CERMICS, 2006
3. Aldous D., and Pitman J. The standard additive coalescent. Ann. Probab. 26 4 (1998) 1703-1726
4. Bertoin J. Lévy Processes (1996), Cambridge University Press, Cambridge
5. Bertoin J. A fragmentation process connected to Brownian motion. Probab. Theory Related Fields 117 (2000) 289-301
6. Bertoin J. Self-similar fragmentations. Ann. Inst. H. Poincaré 38 3 (2000) 319-340
7. Bertoin J. On small masses in self-similar fragmentations. Stochastic Process. Appl. 109 1 (2004) 13-22
8. Bertoin J. Random fragmentation and coagulation processes. Cambridge Studies in Advanced Mathematics No. 102 (2006)
9. Bingham N., Goldie C., and Teugels J. Regular Variation (1987), Cambridge University Press, Cambridge
10. Duquesne T., and Le gall J.-F. Random trees, Lávy processes and spatial branching processes. Astérisque 281 (2002)
11. Haas B. Regularity of formation of dust in self-similar fragmentations. Ann. Inst. H. Poincaré 40 4 (2004) 411-438
12. Jacod J. Calcul stochastique et problèmes de martingales. Lecture Notes in Mathematics vol. 714 (1979), Springer
13. Le gall J.-F., and Le jan Y. Branching processes in Lévy processes: Laplace functionals of snake and superprocesses. Ann. Probab. 26 (1998) 1407-1432
14. Le gall J.-F., and Le jan Y. Branching processes in Lévy processes: The exploration process. Ann. Probab. 26 (1998) 213-252
15. Miermont G. Self-similar fragmentations derived from the stable tree I: splitting at heights. Probab. Theory Related Fields 127 3 (2003) 423-454
16. Miermont G. Self-similar fragmentations derived from the stable tree II: splitting at nodes. Probab. Theory Related Fields 131 3 (2005) 341-375
17. Williams D. Lévy's downcrossing theorem. Z. Wahrscheinlichkeitstheor. Verw. Geb. 40 2 (1977) 157-158