@article{AIHPB_2000__36_4_407_0, author = {Barral, Julien}, title = {Differentiability of multiplicative processes related to branching random walks}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {407--417}, publisher = {Gauthier-Villars}, volume = {36}, number = {4}, year = {2000}, mrnumber = {1785388}, zbl = {0977.60077}, language = {en}, url = {http://archive.numdam.org/item/AIHPB_2000__36_4_407_0/} }
TY - JOUR AU - Barral, Julien TI - Differentiability of multiplicative processes related to branching random walks JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2000 SP - 407 EP - 417 VL - 36 IS - 4 PB - Gauthier-Villars UR - http://archive.numdam.org/item/AIHPB_2000__36_4_407_0/ LA - en ID - AIHPB_2000__36_4_407_0 ER -
%0 Journal Article %A Barral, Julien %T Differentiability of multiplicative processes related to branching random walks %J Annales de l'I.H.P. Probabilités et statistiques %D 2000 %P 407-417 %V 36 %N 4 %I Gauthier-Villars %U http://archive.numdam.org/item/AIHPB_2000__36_4_407_0/ %G en %F AIHPB_2000__36_4_407_0
Barral, Julien. Differentiability of multiplicative processes related to branching random walks. Annales de l'I.H.P. Probabilités et statistiques, Tome 36 (2000) no. 4, pp. 407-417. http://archive.numdam.org/item/AIHPB_2000__36_4_407_0/
[1] Martingale convergence in the branching random walk, J. Appl. Probab. 14 (1977) 25-37. | MR | Zbl
,[2] Growth rates in the branching random walk, Z. Wahrsch. Verw. Gebiete 48 (1979) 17-34. | MR | Zbl
,[3] Uniform convergence of martingales in the one-dimensional branching random walk, in: I.V. Basawa, R.L. Taylor (Eds.), Selected Proceedings of the Sheffield Symposium on Applied Probability, 1989, IMS Lectures Notes- Monograph Series, Vol. 18,1991, pp. 159-173. | MR | Zbl
,[4] Uniform convergence of martingales in the branching random walk, Ann. Probab. 20 (1992) 137-151. | MR | Zbl
,[5] Fixed points of the smoothing transformation, Z. Wahrsch. Verw. Gebiete 64 (1983) 275-301. | MR | Zbl
, ,[6] Sur la loi des grands nombres pour les variables aléatoires de Bernouilli attachées à un arbre dyadique, C. R. Acad. Sci. Paris 278 (1973) 963-964. | MR | Zbl
, , ,[7] Sur certaines martingales de Benoit Mandelbrot, Adv. Math. 22 (1976) 131-145. | MR | Zbl
, ,[8] The first birth problem for an age-dependent branching process, Ann. Probab. 3 (1975) 790-801. | MR | Zbl
,[9] Sur une équation fonctionnelle et ses applications: une extension du théorème de Kesten-Stigum concernant des processus de branchement, Adv. Appl. Probab. 29 (2) (1997) 353-373. | MR | Zbl
,[10] Self-similar cascades and the branching random walk, Preprint, Univ. Rennes 1, 1997.
,[11] A simple path to Biggins' martingale convergence, in: K.B. Athreya, P. Jagers (Eds.), Classical and Modem Branching Processes, IMA Volumes in Mathematics and its Applications, Vol. 84, Springer, Berlin, 1997, pp. 217-222. | MR | Zbl
,[12] Intermittent turbulence in self-similar cascades, divergence of hight moments and dimension of the carrier, J. Fluid. Mech. 62 (1974) 331-358. | Zbl
,[13] Multiplications aléatoires itérées et distributions invariantes par moyennes pondérées, C. R. Acad. Sci. Paris 278 (1974) 289-292, 355-358. | Zbl
,[14] Martingales à Temps Discret, Masson et Cie, Paris, 1972. | MR
,[15] Smoothness and differentiability of functions, Annales Univ. Sci. Budapest. III-IV (1960-1961) 295-307. | MR | Zbl
, ,[16] Weak convergence of stochastic processes whoose trajectories have no discontinuity of the second kind and the "heuristic" approach to the Kolmogorov-Smirnov tests, Theory Probab. Appl. 1 (1956) 140-144.
,[17] Inequalities for the rth absolute moment of sum of random variables, 1 ≤ r ≤ 2, Ann. Math. Statist. 36 (1965) 299-303. | MR | Zbl
, ,[18] Limit theorem for a class of branching processes, in: J. Chover (Ed.), Markov Processes and Potential Theory, Wiley, New York, 1967, pp. 205-232. | MR | Zbl
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