Products of Random Weights Indexed by Galton-Watson Trees
Publications de l'Institut de recherche mathématiques de Rennes, Fascicule de probabilités, no. 2 (1996-1997), article no. 5, 24 p. 
@article{PSMIR_1996-1997___2_A5_0,
     author = {Liu, Quansheng},
     title = {Products of {Random} {Weights} {Indexed} by {Galton-Watson} {Trees}},
     journal = {Publications de l'Institut de recherche math\'ematiques de Rennes},
     eid = {5},
     pages = {1--24},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {2},
     year = {1996-1997},
     language = {en},
     url = {http://archive.numdam.org/item/PSMIR_1996-1997___2_A5_0/}
}
TY  - JOUR
AU  - Liu, Quansheng
TI  - Products of Random Weights Indexed by Galton-Watson Trees
JO  - Publications de l'Institut de recherche mathématiques de Rennes
PY  - 1996-1997
SP  - 1
EP  - 24
IS  - 2
PB  - Département de Mathématiques et Informatique, Université de Rennes
UR  - http://archive.numdam.org/item/PSMIR_1996-1997___2_A5_0/
LA  - en
ID  - PSMIR_1996-1997___2_A5_0
ER  - 
%0 Journal Article
%A Liu, Quansheng
%T Products of Random Weights Indexed by Galton-Watson Trees
%J Publications de l'Institut de recherche mathématiques de Rennes
%D 1996-1997
%P 1-24
%N 2
%I Département de Mathématiques et Informatique, Université de Rennes
%U http://archive.numdam.org/item/PSMIR_1996-1997___2_A5_0/
%G en
%F PSMIR_1996-1997___2_A5_0
Liu, Quansheng. Products of Random Weights Indexed by Galton-Watson Trees. Publications de l'Institut de recherche mathématiques de Rennes, Fascicule de probabilités, no. 2 (1996-1997), article  no. 5, 24 p. http://archive.numdam.org/item/PSMIR_1996-1997___2_A5_0/

Athreya, K.B. (1971) : A note on a functional equation arising in Galton-Watson branching processes. J. Appl. Prob., 8, 589-598. | MR | Zbl

Athreya, K.B. and Ney, P.E. (1972) : Branching processes. Springer, Berlin. | MR | Zbl

Barrai J. (1997): Continuté, Moments d'ordres négatifs et Analyse Multifractale de cascades multiplicatives de Mandelbrot. Thèse, Univ. Paris-Sud, Orsay.

Ben Nasr, F. (1987) : Mesures aléatoires de Mandelbrot associées à des substitutions. CRAS, Sér. I, 304, 255-258. | MR | Zbl

Biggins, J.D. (1977) : Martingale convergence in the branching random walk. J. Appl. Prob. 14, 25-37. | MR | Zbl

Biggins, J.D. and Bingham, N.H. (1993) : Large deviations in the supercritical branching process. Adv. Appl. Prob. 25, 757-772. | MR | Zbl

Bingham, N.H. and Doney,R.A. (1974): Asymptotic properties of supercritical ranching processes I: The Galton-Watson process. Adv. Appl. Prob., 6, 711-731. | MR | Zbl

Bingham, N.H. and Doney, R.A. (1975): Asymptotic properties of supercritical branching processes II: Crump-Mode and Jirina processes. Adv. Appl. Prob., 7, 66-82. | MR | Zbl

Bingham, N.H., Goldie, C.M. and Teugels, J.L. (1987) : Regular variation. Cambridge: Cambridge University Press. | MR | Zbl

Chauvin, B. and Rouault, A. (1996) Boltzmann-Gibbs weights in the branching random walk. IMA Congress on Branching Processes n°84. Lecture Notes in Maths. | MR | Zbl

Collet, P. and Koukiou, F. (1992) : Large deviations for multiplicative chaos. Comm. Math. Phys. 147, 329-342. | MR | Zbl

Crump, K. and Mode, C.J. (1968-1969) : A general age-dependent branching process J. Math. Anal. Appl., 24, 497-508 and 25, 8-17. | MR | Zbl

Doney, R.A. (1972) : A limit theorem for a class of supercritical branching processes. J. Appl. Prob., 9, 707-724. | MR | Zbl

Doney, R.A. (1973) : On a functional equation for general branching processes. J. Appl. Prob., 10, 497-508. | MR | Zbl

Durrett, R. and Liggett, T. (1983) : Fixed points of the smoothing transformation. Z. Wahrsch. verw. Gebeite, 64, 275-301. | MR | Zbl

Falconer, K.J. (1986) : Random fractals. Math.Proc.Camb.Phil.Soc, 100, 559-582. | MR | Zbl

Falconer, K.J. (1987) : Cut set sums and tree processes. Proc. Amer. Math. Soc. (2), 101, 337-346. | MR | Zbl

Feller, W. (1970): An introduction to probability theory and its applications, vol.11, 2nd. ed. John Wiley & Sons, New York. | MR | Zbl

Graf, S. Mauldin, R.D, and Williams, S.C. (1988) : The exact Hausdorff dimension in random recursive constructions. Mem. Amer. Math. Soc. 71, 381. | MR | Zbl

Grintsevichyus, A.K. (1974): On the continuity of a sum of dependent variables connected with independent walks on lines. Theory Prob. Appl. 19, 163-168. | MR | Zbl

Grintsevichyus (1975): One limit distribution for a random walk on the line. Lithunian Math. Trans. 15, 580-589. | Zbl

Guivarc'H, Y. (1990) : Sur une extension de la notion de loi semi-stable. Ann. IHP 26, 261-285. | Numdam | MR | Zbl

Harris, T.E. (1948) : Branching processes, Ann. Math. Stat. 19, 474-494. | MR | Zbl

Holley, R. and Liggett, T. (1981) : Generalized potlach and smoothing processes. Z. Wahrsch. verw. Gebeite, 55, 165-195. | MR | Zbl

Holley, R. and Waymire, E.C. (1992) : Multifractal dimensions and scaling exponents for strongly bounded cascades. Ann. Appl. Prob. 2, 819-845. | MR | Zbl

Kahane, J.P. (1987) : Multiplications aléatoires et dimension de Hausdorff. Ann. IHP, Sup. au no. 2, vol. 23, 289-296. | Numdam | MR | Zbl

Kahane, J.P. and Peyrière (1976) : Sur certaines martingales de Benoit Mandelbrot. Adv. Math., 22, 131-145. | MR | Zbl

Kesten, H. (1973): Random difference equations and renewal theory for products of random matrices. Acta Math. 131, 207-248. | MR | Zbl

Kesten, H and Stigum, B.P. (1966): A limit theorem for multidimensional Galton- Watson processes. Ann. Math. Statist. 37, 1211-1223. | MR | Zbl

Liu, Q. (1993) : Sur quelques problèmes à propos des processus de branchement, des flots dans les réseaux et des mesures de Hausdorff associées. Thèse, Université Paris 6.

Liu, Q. (1996): The exact Hausdorff dimension of a branching set. Prob. Th. Rel. Fields, 104; 1996, 515-538. | MR | Zbl

Liu, Q. (1996): The growth of an entire characteristic function and the tail probabilities of the limit of a tree martingale. In Trees. Progress in Probability, vol.40, pp 51-80, 1996, Birkhöuser: Verlag Basel. Eds.: B.Chauvin, S.Cohen, A.Rouault. | MR | Zbl

Liu, Q. (1997a) : Sur une équation fonctionnelle et ses applications : une extension du théorème de Kesten-Stigum concernant des processus de branchement. To appear in Adv. Appl. Prob. 1997. | MR | Zbl

Liu, Q. (1997b) : Fixed points of a generalized smoothing transformation and applications to branching processes. To appear in Adv. Appl. Prob. 1997. | MR | Zbl

Liu, Q and Rouault, A. (1996): On two measures defined on the boundary of a branching tree. In "Classical and modern branching processes", ed. K.B. Athreya and P. Jagers. IMA Volumes in Mathematics and its applications, vol. 84, 1996, pp. 187-202. Springer-Verlag. | MR | Zbl

Mandelbrot, B. (1974) : Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire. CRAS Paris vol. 278, 325-346 et 355-358. | MR | Zbl

Mauldin, R.A. and Williams, S.C. (1986) : Random constructions, asymptotic geometric and topological properties. Trans. Amer. Math. Soc. 295, 325-346. | MR | Zbl

Seneta, E. (1968) : On recent theorems concerning the supercritical Galton- Watson process. Ann. Math. Stat. 39, 2098-2102. | MR | Zbl

Seneta, E. (1969) : Functional equations and the Galton-Watson process. Adv. Appl. Prob. 1, 1-42. | MR | Zbl

Waymire, E.C. and Williams, S.C. (1995) : Multiplicative cascades : dimension spectra and dependence. J. of Fourier Analysis and Appl., Kahane Special Issue. | MR | Zbl