Regularity of formation of dust in self-similar fragmentations

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 40, Issue 4, 2004, Pages 411-438

  Haas, Bénédicte ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Fragmentation; H lder continuity; Lebesgue density; Loss of mass to dust; Self similarity

Indexed keywords

EID: 2942593709     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2003.11.002     Document Type: Article

References (24)

1. Aldous D.J. Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists Bernoulli 5 1999 3-48
2. Artin E. The Gamma Function 1964 Holt, Rinehart, and Winston New York
3. Berestycki J. Ranked fragmentations ESAIM P&S 6 2002 157-176
4. Bertoin J. Subordinators: Examples and applications in: Bernard P. (Ed.), Lectures on Probability Theory and Statistics, Ecole d'été de probabilités de St-Flour XXVII Lect. Notes in Maths. vol. 1717 1999 1-91 Springer Berlin
5. Bertoin J. Homogeneous fragmentation processes Probab. Theory Related Fields 121 3 2001 301-318
6. Bertoin J. Self-similar fragmentations Ann. Inst. Henri Poincaré 38 2002 319-340
7. Bertoin J. The asymptotic behavior of fragmentation processes J. Eur. Math. Soc. 5 2003 395-416
8. Bertoin J. On small masses in self-similar fragmentations Stochastic Process. Applic. 109 2004 13-22
9. Bertoin J. Yor M. On subordinators, self-similar Markov processes and factorization of the exponential variable Elect. Comm. Probab. 6 10 2001 95-106
10. Beysens D. Campi X. Pefferkorn E. (Eds.), Proceedings of the Workshop: Fragmentation Phenomena Les Houches Series 1995 World Scientific
11. Bingham N.H. Goldie C.M. Teugels J.L. Regular Variation 1987 Cambridge University Press
12. Bochner S. Chandrasekharan K. Fourier Transforms 1949 Princeton University Press
13. Carmona P. Petit F. Yor M. On the distribution and asymptotic results for exponential functionals of Lévy processes in: Yor M. (Ed.), Exponential Functionals and Principal Values Related to Brownian Motion 1997 73-121 Biblioteca de la Revista Matematica IberoAmericana
14. Falconer K. The Geometry of Fractal Sets 1986 Cambridge University Press
15. Filippov A.F. On the distribution of the sizes of particles which undergo splitting Theory Probab. Appl. 6 1961 275-294
16. Fournier N. Giet J.S. On small particles in coagulation-fragmentation equations J. Statist. Phys. 111 5 2003 1299-1329
17. Haas B. Loss of mass in deterministic and random fragmentations Stochastic Process. Appl. 106 2 2003 245-277
18. B. Haas, G. Miermont, The genealogy of self-similar fragmentations with negative index as a continuum random tree, Electron. J. Probab., submitted for publication
19. Jeon I. Stochastic fragmentation and some sufficient conditions for shattering transitions J. Korean Math. Soc. 39 4 2002 543-558
20. Kingman J.F.C. The coalescent Stochastic Process. Appl. 13 1982 235-248
21. Miermont G. Self-similar fragmentations derived from the stable tree I: splitting at heights Probab. Theory Related Fields 127 2003 423-454
22. Revuz D. Yor M. Continuous Martingales and Brownian Motion third ed. 1998 Springer
23. Sato K.-I. Lévy Processes and Infinitely Divisible Distributions 1999 Cambridge University Press
24. Stein E.M. Singular Integrals and Differentiability Properties of Functionals 1970 Princeton University Press