Differentiability of multiplicative processes related to branching random walks

Julien Barral

Annales de l'I.H.P. Probabilités et statistiques (2000)

  • Volume: 36, Issue: 4, page 407-417
  • ISSN: 0246-0203

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Barral, Julien. "Differentiability of multiplicative processes related to branching random walks." Annales de l'I.H.P. Probabilités et statistiques 36.4 (2000): 407-417. <http://eudml.org/doc/77665>.

@article{Barral2000,
author = {Barral, Julien},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {branching random walks; multiplicative cascades; martingales; functional equations},
language = {eng},
number = {4},
pages = {407-417},
publisher = {Gauthier-Villars},
title = {Differentiability of multiplicative processes related to branching random walks},
url = {http://eudml.org/doc/77665},
volume = {36},
year = {2000},
}

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
PB - Gauthier-Villars
VL - 36
IS - 4
SP - 407
EP - 417
LA - eng
KW - branching random walks; multiplicative cascades; martingales; functional equations
UR - http://eudml.org/doc/77665
ER -

References

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  2. [2] J.D. Biggins, Growth rates in the branching random walk, Z. Wahrsch. Verw. Gebiete48 (1979) 17-34. Zbl0387.60092MR533003
  3. [3] J.D. Biggins, 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. Zbl0770.60077MR1193068
  4. [4] J.D. Biggins, Uniform convergence of martingales in the branching random walk, Ann. Probab.20 (1992) 137-151. Zbl0748.60080MR1143415
  5. [5] R. Durrett, Th. Liggett, Fixed points of the smoothing transformation, Z. Wahrsch. Verw. Gebiete64 (1983) 275-301. Zbl0506.60097MR716487
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  7. [7] J.-P. Kahane, J. Peyrière, Sur certaines martingales de Benoit Mandelbrot, Adv. Math.22 (1976) 131-145. Zbl0349.60051MR431355
  8. [8] J.F.C. Kingman, The first birth problem for an age-dependent branching process, Ann. Probab.3 (1975) 790-801. Zbl0325.60079MR400438
  9. [9] Q. Liu, 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. Zbl0901.60055MR1450934
  10. [10] Q. Liu, Self-similar cascades and the branching random walk, Preprint, Univ. Rennes1, 1997. 
  11. [11] R. Lyons, 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. Zbl0897.60086MR1601749
  12. [12] B. Mandelbrot, Intermittent turbulence in self-similar cascades, divergence of hight moments and dimension of the carrier, J. Fluid. Mech.62 (1974) 331-358. Zbl0289.76031
  13. [13] B. Mandelbrot, Multiplications aléatoires itérées et distributions invariantes par moyennes pondérées, C. R. Acad. Sci. Paris278 (1974) 289-292, 355-358. Zbl0276.60096
  14. [14] J. Neveu, Martingales à Temps Discret, Masson et Cie, Paris, 1972. MR402914
  15. [15] E.M. Stein, A. Zygmund, Smoothness and differentiability of functions, Annales Univ. Sci. Budapest.III-IV (1960-1961) 295-307. Zbl0104.04803MR132135
  16. [16] N.N. Tchentov, 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. [17] B. Von Bahr, C.-G. Esseen, Inequalities for the rth absolute moment of sum of random variables, 1 ≤ r ≤ 2, Ann. Math. Statist.36 (1965) 299-303. Zbl0134.36902MR170407
  18. [18] S. Watanabe, Limit theorem for a class of branching processes, in: J. Chover (Ed.), Markov Processes and Potential Theory, Wiley, New York, 1967, pp. 205-232. Zbl0253.60072MR237007

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