Fragmentation associated with Lévy processes using snake

Probability Theory and Related Fields

Volumn 141, Issue 1-2, 2008, Pages 113-154

  Abraham, Romain ^a   Delmas, Jean François ^b  

^a UNIVERSITÉ D'ORLÉANS   (France)

^b UNIVERSITÉ PARIS EST   (France)

Author keywords

Dislocation measure; Fragmentation; L vy snake; Special Markov property; Stable processes

Indexed keywords

EID: 38849089422     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-007-0081-2     Document Type: Article

References (19)

1. Abraham R and Delmas J.-F. (2007). Asymptotics for the small fragments of the fragmentation at nodes. Bernoulli 13(1): 211-228
2. Abraham R. and Delmas J.-F. (2007). Feller property and infinitesimal generator of the exploration process. J. Theor. Probab. 20(3): 355-370
3. Abraham, R., Serlet, L.: Poisson snake and fragmentation. Elect. J. Probab. 7 (2002)
4. Aldous D. (1993). The continuum random tree III. Ann. Probab. 21(1): 248-289
5. Aldous D. and Pitman J. (1998). The standard additive coalescent. Ann. Probab. 26(4): 1703-1726
6. Bertoin J. (1996). Lévy processes. Cambridge University Press, Cambridge
7. Bertoin J. (2000). A fragmentation process connected to Brownian motion. Probab. Th. Rel. Fields 117: 289-301
8. Bertoin J. (2000). Self-similar fragmentations. Ann. Inst. Henri Poincaré 38(3): 319-340
9. Bertoin, J.: Random fragmentation and coagulation processes. In: Cambridge Studies in Advanced Mathematics, vol. 102. Cambridge University Press, Cambridge (2006)
10. Delmas J.-F. (2007). Fragmentation at height associated to Lévy processes. Stoch. Process. Appl. 117(3): 297-311
11. Duquesne, T., Le Gall, J.-F.: Random trees, Lévy processes and spatial branching processes, vol. 281. AstTrisque (2002)
12. Duquesne T. and Le Gall J.-F. (2005). Probabilistic and fractal aspects of Lévy trees. Probab. Th. Rel. Fields 131(4): 553-603
13. Jacod, J.: Calcul stochastique et problèmes de martingales. In: Lecture Notes in Mathematics, vol. 714. Springer, Heidelberg (1979)
14. Le Gall J.-F. and Le Jan Y. (1998). Branching processes in Lévy processes: Laplace functionals of snake and superprocesses. Ann. Probab. 26: 1407-1432
15. Le Gall J.-F. and Le Jan Y. (1998). Branching processes in Lévy processes: The exploration process. Ann. Probab. 26: 213-252
16. Miermont, G.: Ordered additive coalescent and fragmentations and stable subordinators. Elect. J. Probab. 6 (2001)
17. Miermont G. (2003). Self-similar fragmentations derived from the stable tree I: splitting at heights. Probab. Th. Rel. Fields 127(3): 423-454
18. Miermont G. (2005). Self-similar fragmentations derived from the stable tree II: splitting at nodes. Probab. Th. Rel. Fields 131(3): 341-375
19. Parthasarathy, K.R.: Probability measures on metric spaces. Probability and Mathematical Statistics, No. 3. Academic, New York (1967)