Download this PDF file Fullscreen Fullscreen Off
References
- D. J. Aldous (1999). Deterministic and stochastic models for coalescence (aggregation, coagulation): a review of the mean-field theory for probabilists. Bernoulli 5 , 3-48. Math. Review 2001c:60153
- D. J. Aldous and J. Pitman (1998). The standard additive coalescent. Ann. Probab. 26 , 1703-1726. Math. Review 2000d:60121
- Y. Baryshnikov and A. Gnedin (2001). Counting intervals in the packing process. Ann. Appl. Probab. 11 , 863-877. Math. Review 2003a:60014
- J. Bertoin (2000). A fragmentation process connected to Brownian motion. Probab. Theory Relat. Fields 117 , 289-301. Math. Review 2002b:60136
- J. Bertoin (2001). Homogeneous fragmentation processes, Probab. Theory Relat. Fields 121 , 301-318. Math. Review 2002j:60127
- J. Bertoin (2002). Self-similar fragmentations. Ann. Inst. Henri Poincare 38 , 319-340. Math. Review 2003h:60109
- J. Bertoin (2003). The asymptotic behavior of fragmentation processes. J. Euro. Math. Soc. 5 , 395-416. MR2017852
- J. Bertoin (2004). On small masses in self-similar fragmentations. Stochastic Process. Appl. 109 , 13-22. MR2024841
- J. Bertoin and M.-E. Caballero (2002). Entrance from $0+$ for increasing semi-stable Markov processes. Bernoulli 8 , 195-205. Math. Review 2003c:60071
- J. Bertoin and A. Rouault (2003). Discretization methods for homogeneous fragmentations. Preprint.
- J. Bertoin and M. Yor (2001). On subordinators, self-similar Markov processes, and some factorizations of the exponential law. Elect. Commun. Probab. 6 , 95-106. Available at http://www.math.washington.edu/ejpecp/ecp6contents.html. Math. Review 2002k:60097
- J. Bertoin and M. Yor (2004). On the exponential functionals of L 'evy processes. In preparation.
- D. Beysens, X. Campi, and E. Pefferkorn. (1995). Fragmentation Phenomena . World Scientific, Singapore.
- J. D. Biggins (1977). Martingale convergence in the branching random walk. J. Appl. Probability 14 , no. 1, 25--37. MR0433619
- J. D. Biggins (1992). Uniform convergence of martingales in the branching random walk Ann. Probab. 20 , 137-151. Math. Review 93b:60094
- M. D. Brennan and R. Durrett (1986). Splitting intervals, Ann. Probab. 14 , 1024-1036. Math. Review 87k:60088
- M. D. Brennan and R. Durrett (1987). Splitting intervals II. Limit laws for lengths. Probab. Theory Related Fields 75 , 109--127. Math. Review 88k:60058
- A. F. Filippov (1961). On the distribution of the sizes of particles which undergo splitting. Th. Probab. Appl. 6 , 275-293. Math. Review MR0140159
- A. Iserles and Y. Liu (1997) Integro-differential equations and generalized hypergeometric functions, J. Math. Anal. Appl. 208 , 404-424. Math. Review 98f:34095
- A.N. Kolmogorov (1941) "U ber das logarithmisch normale Verteilungsgesetz der Dimensionen der Teilchen bei Zerst "u kelung, Soviet Doklady 31 , 99-101. MR0004415
- J. Lamperti (1972). Semi-stable Markov processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 22 , 205--225. MR0307358
- Q. Liu (2000) On generalized multiplicative cascades, Stoch. Proc. Appl. 86 , 263-286. Math. Review 2001b:60102
- O. Marichev (1983) Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables , Ellis Horwood, Chichester. Math. Review 84f:00017
- R.D. Mauldin and S.C. Williams (1986) Random recursive constructions: asymptotic geometric and topological properties, Trans. Amer. Math. Soc. 295 , 325-426. MR0831202 (87j:60027)
- G. Miermont (2004). Self-similar fragmentations derived from the stable tree II: splitting at hubs. Probab. Theory Relat. Fields . Math. Review MR2018924
- G. Miermont and J. Schweinsberg (2003). Self-similar fragmentations and stable subordinators. In: S'eminaire de Probabilit'es XXXVII , Lecture Notes in Maths. 1832, pp. 333-359. Springer, Berlin. MR2053052
- J. Neveu (1987). Multiplicative martingales for spatial branching processes. In Seminar on Stochastic Processes, Progr. Probab. Statist. 15 pp. 223--242. Birkh"auser, Boston. Math. Review 91f:60144
- U. R"oesler (1992) A fixed point theorem for distributions, Stoch. Proc. Appl. 42 , 195-214. Math. Review 93k:60038
- S.M. Ross (1983). Stochastic Processes, Wiley, N.Y. Math. Review 84m:60001
- J. Schweinsberg (2001). Applications of the continuous-time ballot theorem to Brownian motion and related processes. Stochastic Process. Appl. 95, 151--176. Math. Review 2002e:60076
- K. Uchiyama (1982). Spatial growth of a branching process of particles living in $R^d $. Ann. Probab. 10 , 896-918. Math. Review 84d:60127

This work is licensed under a Creative Commons Attribution 3.0 License.