Uniform dimension results of multi-parameter stable processes

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 42, Issue 9, 1999, Pages 932-944

  Lin, Huonan ^a  

^a FUJIAN NORMAL UNIVERSITY   (China)

Author keywords

Processes with independent increments; Stable (N, d, ) process; Uniform dimension

Indexed keywords

EID: 0042224509     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02880385     Document Type: Article

References (14)

1. Kaufman, R., Une propiété métriqé du mouvement brownien, C. R. Acad. Sci. Paris, Sér A, 1969, 268: 727.
2. Taylor, S. J., The measure theory of random fractal, Math., Proc. Cambridge Phil. Soc., 1986, 100(3): 382.
3. Hu Dihe, Liu Luqin, Xiao Yimin et al., The random fractal, Advances in Mathematics (in Chinese), 1995, 24(3): 193.
4. Hawkes, J., Some dimension theorems for the sample functions of stable processes, Indiana Univ. Math. J., 1971, 20: 733.
5. Hawkes, J., Pruitt, W. E., Uniform dimension results for processes with independent increments, Z. Wahrsch., 1974, 28: 277.
6. Blumenthal, R. M., Getoor, R. K. A dimension theorem for sample functions of stable processes, Illinois Math. J., 1960, 4: 370.
7. Monrad, D., Pitt, L. D., Local nondeterminism and Hausdorff dimension, Progress in Probability and Statistics, Serminar on Stochastic Processes (eds. Cinlor E, Chung K L., Getoor R K,), Boston, Birkhäuser: 1986, 163-189.
8. Mountford, T. S., Uniform dimension results for the Brownian sheet, Ann. Probab., 1989, 17: 1454.
9. Liu Huonan, Zhuang Xingwu, A new proof of the uniform dimension results for multi-parameter Wiener processes, Fujian Teachers Univ. J. (natural science) (in Chinese), 1994, 10(4): 27.
10. Perkins, E. A., Taylor, S. J., Uniform measure results for the image of subset under Brownian motion, Probab. Th. Rel. Fields, 1987, 76(3): 257.
11. Nolan, J. P., Path properties of index-β stable fields, Ann. Probab., 1988, 16(4): 1596.
12. Xiao Yimin, Lin Huonan, Dimension properties of sample paths of self-similar process, Acta Math. Sinica, New Series, 1994, 10(3): 289.
13. Ehm, W., Sample function properties of multi-parameter stable processes, Z. Wahrsch, 1981, 56(2): 195.
14. Adler, R. J., The uniform dimension of the level sets of a Brownian sheet, Ann. Probab., 1978, 6(2): 509.