Regularity of formation of dust in self-similar fragmentations
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 4, pp. 411-438.
@article{AIHPB_2004__40_4_411_0,
     author = {Haas, B\'en\'edicte},
     title = {Regularity of formation of dust in self-similar fragmentations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {411--438},
     publisher = {Elsevier},
     volume = {40},
     number = {4},
     year = {2004},
     doi = {10.1016/j.anihpb.2003.11.002},
     mrnumber = {2070333},
     zbl = {1041.60058},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.002/}
}
TY  - JOUR
AU  - Haas, Bénédicte
TI  - Regularity of formation of dust in self-similar fragmentations
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2004
SP  - 411
EP  - 438
VL  - 40
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.002/
DO  - 10.1016/j.anihpb.2003.11.002
LA  - en
ID  - AIHPB_2004__40_4_411_0
ER  - 
%0 Journal Article
%A Haas, Bénédicte
%T Regularity of formation of dust in self-similar fragmentations
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2004
%P 411-438
%V 40
%N 4
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.002/
%R 10.1016/j.anihpb.2003.11.002
%G en
%F AIHPB_2004__40_4_411_0
Haas, Bénédicte. Regularity of formation of dust in self-similar fragmentations. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 4, pp. 411-438. doi : 10.1016/j.anihpb.2003.11.002. http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.002/

[1] D.J Aldous, Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists, Bernoulli 5 (1999) 3-48. | MR | Zbl

[2] E Artin, The Gamma Function, Holt, Rinehart, and Winston, New York, 1964. | MR | Zbl

[3] J Berestycki, Ranked fragmentations, ESAIM P&S 6 (2002) 157-176. | Numdam | MR | Zbl

[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. | MR | Zbl

[5] J Bertoin, Homogeneous fragmentation processes, Probab. Theory Related Fields 121 (3) (2001) 301-318. | MR | Zbl

[6] J Bertoin, Self-similar fragmentations, Ann. Inst. Henri Poincaré 38 (2002) 319-340. | Numdam | MR | Zbl

[7] J Bertoin, The asymptotic behavior of fragmentation processes, J. Eur. Math. Soc. 5 (2003) 395-416. | MR | Zbl

[8] J Bertoin, On small masses in self-similar fragmentations, Stochastic Process. Applic. 109 (2004) 13-22. | MR | Zbl

[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. | MR | Zbl

[10] Beysens D, Campi X, Pefferkorn E (Eds.), Proceedings of the Workshop: Fragmentation Phenomena, Les Houches Series, World Scientific, 1995.

[11] N.H Bingham, C.M Goldie, J.L Teugels, Regular Variation, Cambridge University Press, 1987. | MR | Zbl

[12] S Bochner, K Chandrasekharan, Fourier Transforms, Princeton University Press, 1949. | MR | Zbl

[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. | MR | Zbl

[14] K Falconer, The Geometry of Fractal Sets, Cambridge University Press, 1986. | MR | Zbl

[15] A.F Filippov, On the distribution of the sizes of particles which undergo splitting, Theory Probab. Appl. 6 (1961) 275-294. | Zbl

[16] N Fournier, J.S Giet, On small particles in coagulation-fragmentation equations, J. Statist. Phys. 111 (5) (2003) 1299-1329. | MR | Zbl

[17] B Haas, Loss of mass in deterministic and random fragmentations, Stochastic Process. Appl. 106 (2) (2003) 245-277. | MR | Zbl

[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. | MR | Zbl

[19] I Jeon, Stochastic fragmentation and some sufficient conditions for shattering transitions, J. Korean Math. Soc. 39 (4) (2002) 543-558. | MR | Zbl

[20] J.F.C Kingman, The coalescent, Stochastic Process. Appl. 13 (1982) 235-248. | MR | Zbl

[21] G Miermont, Self-similar fragmentations derived from the stable tree I: splitting at heights, Probab. Theory Related Fields 127 (2003) 423-454. | MR | Zbl

[22] D Revuz, M Yor, Continuous Martingales and Brownian Motion, Springer, 1998. | Zbl

[23] K.-I Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, 1999. | MR | Zbl

[24] E.M Stein, Singular Integrals and Differentiability Properties of Functionals, Princeton University Press, 1970. | MR | Zbl

Cité par Sources :