Regularity of formation of dust in self-similar fragmentations

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1. [1] D.J Aldous, Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists, Bernoulli5 (1999) 3-48. Zbl0930.60096MR1673235
2. [2] E Artin, The Gamma Function, Holt, Rinehart, and Winston, New York, 1964. Zbl0144.06802MR165148
3. [3] J Berestycki, Ranked fragmentations, ESAIM P&S6 (2002) 157-176. Zbl1001.60078MR1943145
4. [4] J Bertoin, 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, Springer, Berlin, 1999, pp. 1-91. Zbl0955.60046MR1746300
5. [5] J Bertoin, Homogeneous fragmentation processes, Probab. Theory Related Fields121 (3) (2001) 301-318. Zbl0992.60076MR1867425
6. [6] J Bertoin, Self-similar fragmentations, Ann. Inst. Henri Poincaré38 (2002) 319-340. Zbl1002.60072MR1899456
7. [7] J Bertoin, The asymptotic behavior of fragmentation processes, J. Eur. Math. Soc.5 (2003) 395-416. Zbl1042.60042MR2017852
8. [8] J Bertoin, On small masses in self-similar fragmentations, Stochastic Process. Applic.109 (2004) 13-22. Zbl1075.60092MR2024841
9. [9] J Bertoin, M Yor, On subordinators, self-similar Markov processes and factorization of the exponential variable, Elect. Comm. Probab.6 (10) (2001) 95-106. Zbl1024.60030MR1871698
10. [10] Beysens D, Campi X, Pefferkorn E (Eds.), Proceedings of the Workshop: Fragmentation Phenomena, Les Houches Series, World Scientific, 1995. 
11. [11] N.H Bingham, C.M Goldie, J.L Teugels, Regular Variation, Cambridge University Press, 1987. Zbl0617.26001MR898871
12. [12] S Bochner, K Chandrasekharan, Fourier Transforms, Princeton University Press, 1949. Zbl0065.34101MR31582
13. [13] P Carmona, F Petit, M Yor, 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, Biblioteca de la Revista Matematica IberoAmericana, 1997, pp. 73-121. Zbl0905.60056MR1648657
14. [14] K Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1986. Zbl0587.28004MR867284
15. [15] A.F Filippov, On the distribution of the sizes of particles which undergo splitting, Theory Probab. Appl.6 (1961) 275-294. Zbl0242.60050
16. [16] N Fournier, J.S Giet, On small particles in coagulation-fragmentation equations, J. Statist. Phys.111 (5) (2003) 1299-1329. Zbl1018.60061MR1975930
17. [17] B Haas, Loss of mass in deterministic and random fragmentations, Stochastic Process. Appl.106 (2) (2003) 245-277. Zbl1075.60553MR1989629
18. [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. Zbl1064.60076MR2041829
19. [19] I Jeon, Stochastic fragmentation and some sufficient conditions for shattering transitions, J. Korean Math. Soc.39 (4) (2002) 543-558. Zbl1002.60097MR1898911
20. [20] J.F.C Kingman, The coalescent, Stochastic Process. Appl.13 (1982) 235-248. Zbl0491.60076MR671034
21. [21] G Miermont, Self-similar fragmentations derived from the stable tree I: splitting at heights, Probab. Theory Related Fields127 (2003) 423-454. Zbl1042.60043MR2018924
22. [22] D Revuz, M Yor, Continuous Martingales and Brownian Motion, Springer, 1998. Zbl0731.60002
23. [23] K.-I Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, 1999. Zbl0973.60001MR1739520
24. [24] E.M Stein, Singular Integrals and Differentiability Properties of Functionals, Princeton University Press, 1970. Zbl0207.13501MR290095

1. Christina Goldschmidt, Bénédicte Haas, Behavior near the extinction time in self-similar fragmentations I : the stable case