@article{AIHPB_2001__37_2_195_0,
author = {Liu, Quansheng},
title = {Local dimensions of the branching measure on a {Galton-Watson} tree},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
pages = {195--222},
year = {2001},
publisher = {Elsevier},
volume = {37},
number = {2},
zbl = {0986.60080},
language = {en},
url = {https://www.numdam.org/item/AIHPB_2001__37_2_195_0/}
}
TY - JOUR AU - Liu, Quansheng TI - Local dimensions of the branching measure on a Galton-Watson tree JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2001 SP - 195 EP - 222 VL - 37 IS - 2 PB - Elsevier UR - https://www.numdam.org/item/AIHPB_2001__37_2_195_0/ LA - en ID - AIHPB_2001__37_2_195_0 ER -
Liu, Quansheng. Local dimensions of the branching measure on a Galton-Watson tree. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 2, pp. 195-222. https://www.numdam.org/item/AIHPB_2001__37_2_195_0/
[1] , On the limit of a supercritical branching process, J. Appl. Prob. 25A (1988) 215-228. | Zbl | MR
[2] , , Asymptotic properties of supercritical branching processes I: The Galton-Watson process, Adv. Appl. Prob. 6 (1974) 711-731. | Zbl | MR
[3] , , Probability: Independence, Interchageability and Martingales, Springer-Verlag, New York, 1978. | Zbl | MR
[4] , , Defining fractals in a probability space, Ill. J. Math. 38 (1994) 480-500. | Zbl | MR
[5] , On a theorem of Bingham and Doney, J. Appl. Prob. 19 (1982) 217-220. | Zbl | MR
[6] , The extinction time of the inhomogeneous branching Process, in: (Ed.), Branching Processes: Proc. First World Congress, Lecture Notes in Statistics, 99, Springer, Berlin, 1995, pp. 106-117. | Zbl | MR
[7] , Branching Processes, Springer-Verlag, 1963. | MR | Zbl
[8] , A lower Lipschitz condition for the stable subordinator, Z. Wahr. verw. Geb. 17 (1971) 23-32. | Zbl | MR
[9] , Trees generated by a simple branching process, J. London Math. Soc. 24 (1981) 373-384. | Zbl | MR
[10] , , The multifractal structure of stable occupation measure, Stoch. Proc. Appl. 66 (1997) 283-299. | Zbl | MR
[11] , Remarks on the structure of trees with applications to supercritical Galton-Watson processes, in: , (Eds.), Advances in Prob., 5, Dekker, New-York, 1978, pp. 263-268. | Zbl | MR
[12] , Théorie de l'Addition des Variables Aléatoires, Gautier-Villars, Paris, 1954. | JFM
[13] , The exact Hausdorff dimension of a branching set, Prob. Theory Related Fieds 104 (1996) 515-538. | Zbl | MR
[14] , The growth of an entire characteristic function and the tail probabilities of the limit of a tree martingale, Trees, in: , , (Eds.), Trees, Progress in Probability, 40, Birkhäuser, Basel, 1996, pp. 51-80. | Zbl | MR
[15] , Exact packing measure of the boundary of a Galton-Watson tree, Stoch. Proc. Appl. 85 (2000) 19-28. | Zbl | MR
[16] , , On two measures defined on the boundary of a branching tree, in: , (Eds.), Classical and Modern Branching Processes, IMA Volumes in Mathematics and its Applications, 84, Springer-Verlag, 1996, pp. 187-202. | Zbl | MR
[17] , , A uniform limit law for the branching measure on a Galton-Watson tree, Asian J. Math. 3 (1999) 381-386. | Zbl | MR
[18] , , , Ergodic theory on Galton-Watson trees, Speed of random walk and dimension of harmonic measure, Ergodic Theory Dynamical Systems 15 (1995) 593-619. | Zbl | MR
[19] , Arbre et processus de Galton-Watson, Ann. Inst. Henri Poincaré 22 (1986) 199-207. | Zbl | MR | Numdam
[20] , A limit theorem for sample maxima and heavy branches in Galton-Watson trees, J. Appl. Prob. 17 (1980) 539-545. | Zbl | MR
[21] , On the order and the type of entire characteristic functions, Ann. Stat. 33 (1962) 1238-1255. | Zbl | MR
[22] , , Logarithmic multifractal spectrum of stable occupation measure, Stoch. Proc. Appl. 75 (1998) 249-261. | Zbl | MR
[23] , , Multifractal spectra of branching measure on a Galton-Watson tree, Preprint, 1999. | MR






