Limsup random fractals

Electronic Journal of Probability

Volumn 5, Issue , 2000, Pages 1-24

  Khoshnevisan, Davar ^a   Peres, Yuval ^b,c   Xiao, Yimin ^a  

^a Department of Mathematics ^*  (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Hausdorff dimension; Limsup random fractals; Packing dimension

Indexed keywords

EID: 0003028968     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v5-60     Document Type: Article

References (25)

1. A. de Acosta (1983), Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm. Ann. Probab. 11, 78-101.
2. R. J. Adler (1990), An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Institute of Mathematical Statistics, Hayward, CA.
3. N. Bingham, C. Goldie and J. Teugels (1987), Regular Variation. Cambridge University Press.
4. Z. Ciesielski and S. J. Taylor (1962), First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path. Trans. Amer. Math. Soc. 103, 434-450.
5. P. Deheuvels and D. M. Mason (1994), Random fractals generated by oscillations of processes with stationary and independent increments. Probability in Banach spaces 9 (Sandjberg, 1993), 73-89, Progr. Probab., 35, Birkhauser Boston.
6. P. Deheuvels and D. M. Mason (1998), Random fractal functional laws of the iterated logarithm. Studia Sci. Math. Hungar. 34, 89-106.
7. A. Dembo, Y. Peres, J. Rosen and O. Zeitouni (1998), Thick points for spatial Brownian motion: multifractal analysis of occupation measure. Ann. Probab., to appear.
8. A. Dembo and O. Zeitouni (1998), Large Deviations: Techniques and Applications. Second Edition. Applications of Mathematics, 38. Springer-Verlag, New York.
9. J. Hawkes. (1971), On the Hausdorff dimension of the intersection of the range of a stable process with a Borel set. Z. Wahr. verw. Geb., 19, 90-102
10. K. Itô and H. P. McKean, Jr. (1965), Diffusion Processes and Their Sample Paths. Springer-Verlag, Berlin-New York.
11. H. Joyce and D. Preiss (1995), On the existence of subsets of finite positive packing measure. Mathematika 42, 15-24.
12. J-P. Kahane (1985), Some Random Series of Functions, second edition. Cambridge University Press.
13. R. Kaufman (1975), Large increments of Brownian motion. Nagoya Math. J. 56, 139-145.
14. D. Khoshnevisan and Z. Shi (1998), Fast sets and points for fractional Brownian motion. Séminaire de Probabilités XXXIV, to appear.
15. P. Levy (1953), La mesure de Hausdorff de la courbe du mouvement brownien. Giorn. 1st. Ital. Attuari 16, 1-37.
16. M. B. Marcus (1968), Holder conditions for Gaussian processes with stationary increments. Trans. Amer. Math. Soc. 134, 29-52.
17. P. Mattila (1995), Geometry of Sets and Measures in Euclidean Spaces. Cambridge University Press.
18. J. R. Munkres (1975), Topology: A First Course. Prentice-Hall, Inc., Englewood Cliffs, N.J.
19. S. Orey and W. E. Pruitt (1973), Sample functions of the N-parameter Wiener process. Ann. of Probab. 1, 138-163.
20. S. Orey and S. J. Taylor (1974), How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc. 28, 174-192.
21. Y. Peres (1996a). Intersection-equivalence of Brownian paths and certain branching processes. Commun. Math. Phys. 177, 417-434.
22. Y. Peres (1996b), Remarks on intersection-equivalence and capacity-equivalence. Ann. Inst. Henri Poincaré (Physique theorique) 64, 339-347.
23. V. Strassen (1964), An invariance principle for the law of the iterated logarithm. Z. Wahrsch. Verw. Gebiete 3, 211-226.
24. S. J. Taylor (1986), The measure theory of random fractals. Math. Proc. Cambridge Phil. Soc. 100, 383-406.
25. J. B. Walsh (1986), An introduction to stochastic partial differential equations. Ecole d’ete de probabilites de Saint-Flour, XIV-1984, 265-439, Lecture Notes in Math. 1180, Springer, Berlin-New York.