Discretization methods for homogeneous fragmentations

Journal of the London Mathematical Society

Volumn 72, Issue 1, 2005, Pages 91-109

  Bertoin, Jean ^a   Rouault, Alain ^b  

^a INSTITUT UNIVERSITAIRE DE FRANCE   (France)

^b UNIVERSITÉ DE VERSAILLES SAINT QUENTIN EN YVELINES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 31444436068     PISSN: 00246107     EISSN: 14697750     Source Type: Journal    
DOI: 10.1112/S0024610705006423     Document Type: Article

References (27)

1. S. ASMUSSEN and H. HERING, Branching processes (Birkhäuser, Boston, 1983).
2. G. BEN AROUS and A. ROUAULT, 'Laplace asymptotics for reaction-diffusion equations', Probab. Theory Related Fields 97 (1993) 259-285.
3. J. BERESTYCKI, 'Ranked fragmentations', ESAIM Probab. Statist. 6 (2002) 157-176.
4. J. BERTOIN, 'Homogeneous fragmentation processes', Probab. Theory Related Fields 121 (2001) 301-318.
5. J. BERTOIN, 'Self-similar fragmentations', Ann. Inst. H. Poincaré 38 (2002) 319-340.
6. J. BERTOIN, 'The asymptotic behavior of fragmentation processes', J. Europ. Math. Soc. 5 (2003) 395-416.
7. J. BERTOIN and A. ROUAULT, 'Asymptotical behaviour of the presence probability in branching random walks and fragmentations', 2004, arXiv:math.PR/0409547.
8. J. D. BIGGINS, 'Martingale convergence in the branching random walk', J. Appl. Probab. 14 (1977) 25-37.
9. J. D. BIGGINS, 'Uniform convergence of martingales in the branching random walk', Ann. Probab. 20 (1992) 137-151.
10. J. D. BIGGINS and A. E. KYPRIANOU, 'Measure change in multitype branching', Adv. in Appl. Probab. 36 (2004) 544-581.
11. L. CHAUMONT, 'Sur certains processus de Lévy conditionnés à rester positifs', Stochastics Stochastic. Rep. 47 (1994) 1-20.
12. B. CHAUVIN and A. ROUAULT, 'KPP equation and supercritical branching Brownian motion in the subcritical speed area. Application to spatial trees', Probab. Theory Related Fields 80 (1988) 299-314.
13. S. C. HARRIS, 'Travelling waves for the FKPP equation via probabilistic arguments', Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 503-517.
14. J. F. C. KINGMAN, 'Ergodic properties of continuous-time Markov processes and their discrete skeletons', Proc. London Math. Soc. 3 (1963) 593-604.
15. J. F. C. KINGMAN, 'The coalescent', Stochastic Process. Appl. 13 (1982) 236-248.
16. J. F. C. KINGMAN, Poisson processes (Clarendon Press, New York, 1993).
17. A. E. KYPRIANOU, 'Slow variation and uniqueness of solutions to the functional equation in the branching random walk', J. Appl. Probab. 35 (1998) 795-801.
18. A. E. KYPRIANOU, 'A note on branching Lévy processes', Stochastic Process. Appl. 82 (1999) 1-14.
19. A. E. KYPRIANOU, 'Travelling waves solutions to the K-P-P equation: alternative to Simon Harris' probabilistic argument', Ann. Inst. H. Poincaré (B) 40 (2004) 53-72.
20. Q. LIU, 'On generalized multiplicative cascades', Stochastic Process. Appl. 86 (2000) 263-286.
21. R. LYONS, 'A simple path to Biggins' martingale convergence for branching random walk', Classical and modern branching processes (ed. K. B. Athreya and P. Jagers, Springer, New York, 1997) 217-221.
22. R. LYONS, R. PEMANTLE and Y. PERES, 'Conceptual proofs of Llog L criteria for mean behaviour of branching processes', Ann. Probab. 23 (1995) 1125-1138.
23. J. NEVEU, 'Multiplicative martingales for spatial branching processes', Seminar on Stochastic Processes 1987, Progress in Probability Statistics 15 (ed. E. Cinlar, K. L. Chung and R. K. Getoor, Birkhäuser, 1988) 223-242.
24. J. PITMAN, 'Coalescent with multiple collisions', Ann. Probab. 27 (1999) 1870-1902.
25. A. ROUAULT, 'Precise estimates of presence probabilities in the branching random walk', Stochastic Process. Appl. 44 (1993) 27-39.
26. K. SATO, Lévy processes and infinitely divisible distributions (Cambridge University Press, Cambridge, 1999).
27. d', Ann. Probab. 10 (1982) 896-918.