no. 2
Fixed Points of a Generalized Smoothing Transformation and Applications to Branching Processes
Publications de l'Institut de recherche mathématiques de Rennes, no. 2 (1995), article no. 9, 54 p. 
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     author = {Liu, Quansheng},
     title = {Fixed {Points} of a {Generalized} {Smoothing} {Transformation} and {Applications} to {Branching} {Processes}},
     journal = {Publications de l'Institut de recherche math\'ematiques de Rennes},
     eid = {9},
     pages = {1--54},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://www.numdam.org/item/PSMIR_1995___2_A9_0/}
}
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Liu, Quansheng. Fixed Points of a Generalized Smoothing Transformation and Applications to Branching Processes. Publications de l'Institut de recherche mathématiques de Rennes, no. 2 (1995), article  no. 9, 54 p. http://www.numdam.org/item/PSMIR_1995___2_A9_0/

Asmussen, S. and Hering, H. (1983) : Branching processes. Birkhäuser. | MR | Zbl

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

Ben Nasr, F. (1987) : Mesures aléatoires de Mandelbrot associées a des substitutions. C.R. Acad. Sci. Paris, 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

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

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

Chauvin, B. and Rouault, A. (1993) : Boltzmann-Gibbs weights in the branching random walk. Prépublication no.175 du Laboratoire de Probabilités de l'Université Paris VI. | Zbl

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

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

Crump, K. and Mode, C.J. (1969) : A general age-dependent branching process (II). J. Math. Anal. Appl., 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. Wahrscheinlichkeitstheorie verw. Gebiete, 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 processes and tree processes. Math. Proc. Amer. Math. Soc. (2), 101, 337-346. | MR | Zbl

Feller, W. (1971) : An introduction to probability theory and its applications. Vol.2, 2nd ed. John Wiley & Sons. | Zbl

Fortet, R. et Mourier, E (1953) : Convergence de la répartition empirique vers la répartion théorique. Ann. Scient. Ecole Normale Sup. Série 3, tome 70, 266-285. | Numdam | MR | Zbl

Franchi, J. (1993) : Chaos multiplicatif : un traitement simple et complet de la fonction de la partition. Prépublication no. 148 du Laboratoire de Probabilités de l'Université Paris VI. | Numdam | Zbl

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

Guivarc'H, Y. (1990) : Sur une extension de la notion semi-stable, Ann. Inst. Henri Poincaré, (Prob.et Stat.), 26, 261-285. | Numdam | MR | Zbl

Heyde, C.C. (1970) : Extension of a result of Seneta for the supercritical Galton-Watson process. Ann. Math. Statist. 41, 739-742. | MR | Zbl

Holley, R. and Liggett, T. (1981) : Generalized potlatch and smoothing processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 55, 165-195. | MR | Zbl

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

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

Kahane, J.P. and Peyrière J. (1976) : Sur certaines martingales de Benoit Mandelbrot. Adv. Math., 22, 131-145. | 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 asociées. Thèse, Université Paris 6.

Liu, Q. (1994) : Sur une equation fonctionnelle et ses applications : une extension du théorème de Kesten-Stigum concernant des processus de branchement. Prépublication, Université Rennes 1. | Zbl

Liu, Q. (1994a) : Growth of entire characteristic functions and tails in tree martingales, Prépublication, Université Rennes 1.

Mandelbrot, B. (1974) : Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire. C.R. Acad. Sci. Paris, vol.278, Série A, 325-346. | Zbl

Mandelbrot, B. (1974) : Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire : Quelques extensions . C.R. Acad. Sci. Paris, vol.278, Série A, 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

Royer, G. (1984) : Distance de Fortet-Mourier et fonctions log-concaves. Annales Scientifiques de Clermont-Ferrand, n° 78. | Numdam | 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

Seneta, E. (1973) : A Tauberian theorem of E. Landau and W. Feller, Ann. Prob. 1, 1057-1058. | MR | Zbl

Seneta, E. (1974) : Regular varing functions in the theory of simple branching processes. Adv. Appl. Prob. 6, 408-420. | MR | Zbl

Waymire, E.C. and Williams, S.C. (1993) : Multiplicative cascades : spectra and dependence. Preprint, Origon State University and Utah State University.