Self-similar fragmentations

Jean Bertoin

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 3, page 319-340
  • ISSN: 0246-0203

How to cite

top

Bertoin, Jean. "Self-similar fragmentations." Annales de l'I.H.P. Probabilités et statistiques 38.3 (2002): 319-340. <http://eudml.org/doc/77718>.

@article{Bertoin2002,
author = {Bertoin, Jean},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {fragmentation; self-similar fragmentation; exchangeable partition},
language = {eng},
number = {3},
pages = {319-340},
publisher = {Elsevier},
title = {Self-similar fragmentations},
url = {http://eudml.org/doc/77718},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Bertoin, Jean
TI - Self-similar fragmentations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 3
SP - 319
EP - 340
LA - eng
KW - fragmentation; self-similar fragmentation; exchangeable partition
UR - http://eudml.org/doc/77718
ER -

References

top
  1. [1] D.J. Aldous, Exchangeability and related topics, in: Hennequin P.L. (Ed.), Lectures on Probability Theory and Statistics, Ecole d'été de Probabilités de Saint-Flour XIII, Lecture Notes in Maths, 117, Springer, Berlin, 1985. Zbl0562.60042MR883646
  2. [2] D.J. Aldous, Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists, Bernoulli5 (1999) 3-48. Zbl0930.60096MR1673235
  3. [3] D.J. Aldous, J. Pitman, The standard additive coalescent, Ann. Probab.26 (1998) 1703-1726. Zbl0936.60064MR1675063
  4. [4] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. Zbl0861.60003MR1406564
  5. [5] J. Bertoin, A fragmentation process connected to Brownian motion, Probab. Theory Related Fields117 (2000) 289-301. Zbl0965.60072MR1771665
  6. [6] J. Bertoin, Homogeneous fragmentation processes, Preprint, 2000. MR1867425
  7. [7] M.D. Brennan, R. Durrett, Splitting intervals, Ann. Probab.14 (1986) 1024-1036. Zbl0601.60028MR841602
  8. [8] M.D. Brennan, R. Durrett, Splitting intervals. II. Limit laws for lengths, Probab. Theory Related Fields75 (1987) 109-127. Zbl0607.60010MR879556
  9. [9] Ph. 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. 73-126. Zbl0905.60056MR1648657
  10. [10] B. Chauvin, Product martingales and stopping lines for branching Brownian motion, Ann. Probab.19 (1991) 1195-1205. Zbl0738.60079MR1112412
  11. [11] S.N. Evans, J. Pitman, Construction of Markovian coalescents, Ann. Inst. H. Poincaré, Probabilités Statistiques34 (1998) 339-383. Zbl0906.60058MR1625867
  12. [12] J. Jacod, Calcul Stochastique et Problèmes de Martingales, Lecture Notes in Math., 714, Springer, Berlin, 1979. Zbl0414.60053MR542115
  13. [13] J.F.C. Kingman, The coalescent, Stochastic Process. Appl.13 (1982) 235-248. Zbl0491.60076MR671034
  14. [14] J. Lamperti, Semi-stable Markov processes, Z. Wahrscheinlichkeitstheorie verw. Gebiete22 (1972) 205-225. Zbl0274.60052MR307358
  15. [15] J. Pitman, Coalescents with multiple collisions, Ann. Probab.27 (1999) 1870-1902. Zbl0963.60079MR1742892

Citations in EuDML Documents

top
  1. Julien Berestycki, Ranked fragmentations
  2. Jean Bertoin, Fires on trees
  3. Julien Berestycki, Ranked Fragmentations
  4. Gerónimo Uribe Bravo, The falling apart of the tagged fragment and the asymptotic disintegration of the brownian height fragmentation
  5. Bénédicte Haas, Regularity of formation of dust in self-similar fragmentations
  6. M. Escobedo, S. Mischler, M. Rodriguez Ricard, On self-similarity and stationary problem for fragmentation and coagulation models
  7. Anne-Laure Basdevant, On the equivalence of some eternal additive coalescents
  8. Christina Goldschmidt, Bénédicte Haas, Behavior near the extinction time in self-similar fragmentations I : the stable case
  9. S. C. Harris, R. Knobloch, A. E. Kyprianou, Strong law of large numbers for fragmentation processes

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.