The multifractal structure of super-Brownian motion

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 34, Issue 1, 1998, Pages 97-138

  Perkins, Edwin A ^a   Taylor, S James ^b,c  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF VIRGINIA   (United States)

^c UNIVERSITY OF SUSSEX   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21844451949     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(98)80020-4     Document Type: Article

References (23)

1. [BEP] M. T. BARLOW, S. N. EVANS and E. A. PERKINS, Collision Local Times and Measure-valued Processes, Can. J. Math., Vol. 43, 1991, pp. 897-938.
2. [B] A. S. BESICOVICH, A general form of the covering principle and relative differentiation of additive functions, Proc. Camb. Phil. Soc., Vol. 41, 1945, pp. 103-110.
3. [C] C. D. CUTLER, Measure disintegrations with respect to a σ-stable monotone index and the pointwise representation of packing dimension, Rend del Circolo Math di Palermo, Vol. 28, 1992, pp. 319-340.
4. [D1] D. A. DAWSON, Infinitely divisible random measure and superprocesses, in Proc. 1990 Workshop on Stochastic Analysis and Related Topics, 1992, Silivri, Turkey.
5. [D2] D. A. DAWSON Measure-valued Markov Processes, Ecole d'Eté de Probabilités de Saint-Flour XXI, Lecture Notes in Math., Vol. 1541, 1993, pp. 1-260, Springer, Berlin.
6. [DIP] D. A. DAWSON, I. ISCOE and E. A. PERKINS, Super-Brownian motion: Path properties and hitting probabilities, Probab. Theory Related Fields, Vol. 83, 1989, pp. 135-206.
7. [DP] D. A. DAWSON and E. A. PERKINS, Historical Processes, Memoirs of the Amer. Math. Soc., Vol. 93, no. 454, 1991, 179 p.
8. [EP] S. N. EVANS and E. A. PERKINS, Absolute continuity results for superprocesses with some applications, Trans. Amer. Math. Soc., Vol. 325, 1991, pp. 661-681.
9. [F] K. J. FALCONER, Fractal Geometry: mathematics foundations and applications, Wiley, 1990, New York.
10. [Fr] O. FROSTMAN, Potentiel d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions, Medd Lands Univ. Math. Sem., Vol. 3, 1935, pp. 1-188.
11. [Ha] T. C. HALSEY, M. H. JENSEN, L. P. KADANOFF, I. PROCACCIA and B. I. SHRAIMAN, Fractal measures and their singularities, Phys. Rev., Vol. A33, 1986, pp. 1141-1151.
12. [K] F. B. KNIGHT, Essentials of Brownian Motion and Diffusion, American Math. Soc., 1981. Providence.
13. [LG1] J. F. LE GALL, A class of path-valued Markov processes and its applications to superprocesses, Probab. Theory Related Fields, Vol. 95, 1993, pp. 25-46.
14. [LG2] J. F. LE GALL, A path-valued Markov process and its connection with partial differential equations, Proceedings of the First European Congress of Mathematics, (1994)a, pp. 185-212, Birkhäuser, Boston.
15. [LG3] J. F. LE GALL, A lemma on super-Brownian motion with some applications, Festschift in Honor of E.B. Dynkin (M. Friedlin, ed.), 1994b, pp. 237-251, Birkhäuser, Boston.
16. [LPT] J. F. LE GALL, E. A. PERKINS and S. J. TAYLOR, The packing measure of the support of super-Brownian motion, Stoch. Proc. Appl., Vol. 59, 1995, pp. 1-20.
17. [O] L. OLSEN, A multifractal formalism, Advances in Mathematics, Vol. 116, 1995, pp. 82-195.
18. [PI] E. A. PERKINS, The Hausdorff measure of the closed support of super-Brownian motion, Ann. Inst. H. Poincaré, Vol. 25, 1989, pp. 205-224.
19. [P2] E. A. PERKINS, Measure-valued branching diffusions with spatial interactions, Probab. Theory Related Fields, Vol. 94, 1992. pp. 189-245.
20. [PT] E. A. PERKINS and S. J. TAYLOR, Uniform measure results for the image of subsets under Brownian motion, Probab. Theory Related Fields , Vol. 76, 1987, pp. 257-289.
21. [T] S. J. TAYLOR, On the connection between generalized capacities and Hausdorff measures, Proc. Cambridge Philos. Soc., Vol. 57, 1961, pp. 524-531.
22. [TT] S. J. TAYLOR and C. TRICOT, Packing measure and its evaluation for a Brownian path, Trans. Amer. Math. Soc., Vol. 288, 1985, pp. 679-699.
23. [Tr] R. TRIBE, The connected components of the closed support of super-Brownian motion, Probab. Theory Related Fields, Vol. 89, 1991, pp. 75-87.