Hausdorff dimensions of random net fractals

Stochastic Processes and their Applications

Volumn 74, Issue 2, 1998, Pages 235-250

  Liang, Jin Rong ^a   Ren, Fu Yao ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Hausdorff dimensions; Random cookie cutter sets; Random net fractals; Random self similar fractals

Indexed keywords

EID: 0002358163     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0304-4149(97)00104-x     Document Type: Article

References (24)

1. Athreya K.B., Ney P.E. Branching Processes. 1972;Springer, Berlin.
2. Arbeiter M. Random recursive construction of self-similar measures: the non-compact case. Probab. Theory Rel. Fields. 88:1991;497-520.
3. Barnsley M.F. Fractals Everywhere. 1988;Academic Press, New York.
4. Barnsley M.F., Demko S.G. Iterated function systems and the global construction of fractals. Proc. Roy. Soc. London A. 399:1985;243-275.
5. Bedford T., 1989. Applications of dynamical systems theory to fractals. A study of cookie-cutter Cantor sets. Proc. Séminaire de mathématiques Supérieurs, Fractal Geometry and Analysis, Université de Montryéal.
6. Billingsley P. Ergodic Theory and Informations. 1965;Wiley, New York.
7. Falconer K.J. Random fractals. Math. Proc. Camb. Philos. Soc. 100:1986;559-582.
8. Falconer K.J. Fractal Geometry - Mathematical Foundations and Applications. 1990;Wiley, New York.
9. Fristedt B.E. Sample functions of stochastic processes with stationary, independent increments. Adv. Probab. 3:1974;241-396.
10. Graf S., Mauldin R.D., Williams S.C. The exact Hausdorff dimension in random recursive constructions. Mem. Am. Math. Soc. 71:1988;88.
11. Graf S. Statistically self-similar fractals. Probab. Theory Rel. Fields. 74:1987;357-394.
12. Giona M., Roman H.E. Fractional diffusion equation for transport phenomena in random media. Phys. A. 185:1992;87-97.
13. Harris T.E. The Theory of Branching Processes. 1963;Springer, Berlin.
14. Hall P., Heyde, C.C., 1980. Martingale Limit Theory and its Application. New York.
15. d .
16. Mandelbrot B.B. The Fractal Geometry of Nature. 1982;Freeman, New York.
17. Moran P.A.P., 1946. Additive functions of intervals and Hausdorff measure. Proc. Camb. Philos. Soc. 42, 15-23.
18. Mauldin R.D., Williams S.C. Random recursive constructions: asymptotic geometric and topological properties. Trans. Amer. Math. S. 295:1986;325-346.
19. Olsen, L., 1994. Random geometrically graph directed self-similar multifractals, Pitman Research Notes in Math. Series, vol. 307, Longman, Harlow.
20. Patzschke, N., Zähle, U., 1990. Self-similar random measures IV - The recursive construction model of Falconer, Graf and Mauldin and Williams, Math. Nachr. 149.
21. Ren, F.-Y., Yu, Z.-G., to appear. Fractional integral accociated to cookie-cutter set and its physical interpretation. Chinese Proc. Natural Sci.
22. Tsujii Y. Generalized random ergodic theorems and Hausdorff measures of random fractals. Hiroshima Math. J. 19:1989;363-377.
23. Tsujii Y. Markov-self-similar sets. Hiroshima Math. J. 21:1991;491-519.
24. Tohoki H., Tsujii Y. A remark on random fractals. Hiroshima Math. J. 19:1989;563-566.