Exact packing measure on a Galton-Watson tree

Stochastic Processes and their Applications

Volumn 85, Issue 1, 2000, Pages 19-28

  Liu, Quansheng ^a  

^a UNIVERSITÉ DE RENNES 1   (France)

Author keywords

28A78; 28A80; 60J80; Branching measure; Exact packing measure; Galton Watson tree; Hausdorff measure

Indexed keywords

EID: 0012080242     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(99)00062-9     Document Type: Article

References (16)

1. Biggins J.D. Martingale convergence in the branching random walk. J. Appl. Probab. 14:1977;25-37.
2. Bingham N.H. On the limit of a supercritical branching process. J. Appl. Probab. 25A:1988;215-228.
3. Dai C.S., Taylor S.J. Defining fractals in a probability space. Il. J. Math. 38(3):1994;480-500.
4. Falconer K.J. Random fractals. Math. Proc. Cambridge Philos. Soc. 100:1986;559-582.
5. Falconer K.J. Cut set sums and tree processes. Proc. Amer. Math. Soc. 101(2):1987;337-346.
6. Graf, S., Mauldin, R.D., Williams, S.C., 1988. The exact Hausdorff dimension in random recursive constructions. Mem. Amer. Math. Soc. 71, 381.
7. Hawkes J. Trees generated by a simple branching process. J. London Math. Soc. 24:1981;373-384.
8. Kahane, J.P., Peyrière, J. 1976. Sur certaines martingales de Benoit Mandelbrot. Adv. Math. 22, 131-145.
9. Liu, Q.S., 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.
10. Liu Q.S. The exact Hausdorff dimension of a branching set. Probab. Theory Related Fields. 104:1996;515-538.
11. Liu, Q.S., 1996b. The growth of an entire characteristic function and the tail probabilities of the limit of a tree martingale. In: Chauvin, B., Cohen, S., Rouault, A. (Eds.), Trees, Progress in Probability, Vol. 40. Birkhöuser, Basel, pp. 51-80.
12. Liu, Q.S., 1998. Local dimensions of the branching measure on the Galton-Watson tree. Publication 1998, Univ. Rennes 1.
13. Liu, Q.S., 1999. Exact packing of random fractals, in preparation.
14. Liu, Q.S., Rouault, A., 1996. On two measures defined on the boundary of a branching tree. In: Athreya, K.B., Jagers, P. (Eds.), Classical and Modern Branching Processes, IMA Volumes in Mathematics and its Applications, Vol. 84. Springer, Berlin, pp. 187-202.
15. Mandelbrot, B., 1974. Multiplications aléatoires et distributions invariantes par moyenne pondérée aléatoire. C.R. Acad. Sci. Paris Ser. I 278, 289-292 and 355-358.
16. Taylor S.J., Tricot C. Packing measure, and its evaluation for a Brownian path. Trans. Amer. Math. Soc. 288:1985;679-699.