@article{PSMIR_1995___2_A9_0, 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/} }
TY - JOUR AU - Liu, Quansheng TI - Fixed Points of a Generalized Smoothing Transformation and Applications to Branching Processes JO - Publications de l'Institut de recherche mathématiques de Rennes PY - 1995 SP - 1 EP - 54 IS - 2 PB - Département de Mathématiques et Informatique, Université de Rennes UR - http://www.numdam.org/item/PSMIR_1995___2_A9_0/ LA - en ID - PSMIR_1995___2_A9_0 ER -
%0 Journal Article %A Liu, Quansheng %T Fixed Points of a Generalized Smoothing Transformation and Applications to Branching Processes %J Publications de l'Institut de recherche mathématiques de Rennes %D 1995 %P 1-54 %N 2 %I Département de Mathématiques et Informatique, Université de Rennes %U http://www.numdam.org/item/PSMIR_1995___2_A9_0/ %G en %F PSMIR_1995___2_A9_0
Liu, Quansheng. Fixed Points of a Generalized Smoothing Transformation and Applications to Branching Processes. Publications de l'Institut de recherche mathématiques de Rennes, Fascicule de probabilités, no. 2 (1995), article no. 9, 54 p. http://www.numdam.org/item/PSMIR_1995___2_A9_0/
Branching processes. Birkhäuser. | MR | Zbl
and (1983) :A note on a functional equation arising in Galton-Watson branching processes. J. Appl. Prob., 8, 589-598. | MR | Zbl
(1971) :Branching processes. Springer, Berlin. | MR | Zbl
and (1972) :Mesures aléatoires de Mandelbrot associées a des substitutions. C.R. Acad. Sci. Paris, Sér.I, 304, 255-258. | MR | Zbl
(1987) :Martingale convergence in the branching random walk. J.Appl. Prob. 14, 25-37. | MR | Zbl
(1977) :Asympototic properties of supercritical branching processes I : The Galton-Watson process. Adv. Appl. Prob., 6, 711-731. | MR | Zbl
and (1974) :Asympototic properties of supercritical branching processes II: Crump-Mode and Jirina processes. Adv. Appl. Prob., 7, 66-82. | MR | Zbl
and (1975):Boltzmann-Gibbs weights in the branching random walk. Prépublication no.175 du Laboratoire de Probabilités de l'Université Paris VI. | Zbl
and (1993) :Large deviations for multiplicative chaos. Commun. Math. Phys. 147, 329-342. | MR | Zbl
and (1992) :A general age-dependent branching process (I). J. Math. Anal. Appl., 24,497-508. | MR | Zbl
and (1968) :A general age-dependent branching process (II). J. Math. Anal. Appl., 25, 8-17. | MR | Zbl
and (1969) :A limit theorem for a class of supercritical branching processes. J. Appl. Prob., 9, 707-724. | MR | Zbl
(1972) :On a functional equation for general branching processes. J. Appl. Prob., 10, 497-508. | MR | Zbl
(1973) :Fixed points of the smoothing transformation. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 64, 275-301. | MR | Zbl
and (1983) :Random fractals. Math.Proc.Camb.Phil.Soc., 100, 559-582. | MR | Zbl
(1986) :Cut-set processes and tree processes. Math. Proc. Amer. Math. Soc. (2), 101, 337-346. | MR | Zbl
(1987) :An introduction to probability theory and its applications. Vol.2, 2nd ed. John Wiley & Sons. | Zbl
(1971) :Convergence de la répartition empirique vers la répartion théorique. Ann. Scient. Ecole Normale Sup. Série 3, tome 70, 266-285. | Numdam | MR | Zbl
et (1953) :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
(1993) :The exact Hausdorff dimension in random recursive constructions. Mem. Amer. Math. Soc. 71, n°381. | MR | Zbl
, and (1988) :Sur une extension de la notion semi-stable, Ann. Inst. Henri Poincaré, (Prob.et Stat.), 26, 261-285. | Numdam | MR | Zbl
(1990) :Extension of a result of Seneta for the supercritical Galton-Watson process. Ann. Math. Statist. 41, 739-742. | MR | Zbl
(1970) :Generalized potlatch and smoothing processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete, 55, 165-195. | MR | Zbl
and (1981) :Multifractal dimensions and scaling exponents for strongly bounded random cascades. Ann. Appl. Prob. 2, 819-845. | MR | Zbl
and (1992) :Multiplications aléatoires et dimensions de Hausdorff. Ann. Inst. Henri Poincaré, Sup.au no.2, vol.23, p.289-296. | Numdam | MR | Zbl
(1987) :Sur certaines martingales de Benoit Mandelbrot. Adv. Math., 22, 131-145. | MR | Zbl
and (1976) :A limit theorem for multidimensional Galton-Watson processes, Ann. Math. Statist. 37, 1211-1223. | MR | Zbl
and (1966) :Sur quelques problèmes à propos des processus de branchement, des flots dans les réseaux et des mesures de Hausdorff asociées. Thèse, Université Paris 6.
(1993) :Sur une equation fonctionnelle et ses applications : une extension du théorème de Kesten-Stigum concernant des processus de branchement. Prépublication, Université Rennes 1. | Zbl
(1994) :Growth of entire characteristic functions and tails in tree martingales, Prépublication, Université Rennes 1.
(1994a) :Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire. C.R. Acad. Sci. Paris, vol.278, Série A, 325-346. | Zbl
(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
(1974) :Random constructions, asymptotic geometric and topological properties. Trans. Amer. Math. Soc., 295, 325-346. | MR | Zbl
and (1986) :Distance de Fortet-Mourier et fonctions log-concaves. Annales Scientifiques de Clermont-Ferrand, n° 78. | Numdam | MR | Zbl
(1984) :On recent theorems concerning the supercritical Galton-Watson process. Ann. Math. Stat. 39, 2098-2102. | MR | Zbl
(1968) :Functional equations and the Galton-Watson process. Adv. Appl. Prob. 1, 1-42. | MR | Zbl
(1969) :A Tauberian theorem of E. Landau and W. Feller, Ann. Prob. 1, 1057-1058. | MR | Zbl
(1973) :Regular varing functions in the theory of simple branching processes. Adv. Appl. Prob. 6, 408-420. | MR | Zbl
(1974) :Multiplicative cascades : spectra and dependence. Preprint, Origon State University and Utah State University.
and (1993) :