25
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Fractal random measures generated by time continuous branching and diffusion

Pages 107-133 | Published online: 02 May 2007

References

  • Arbeiter , M. 1990 . Random recursive construction of self-similar fractal measures The noncompact case . Probab. Th. Rel. Fields , 88 : 497 – 520 .
  • Arbeiter , M. 1992 . Construction of random fractal measures by branching processes . Stochastics and Stochastics Rep. , 39 : 195 – 212 .
  • Arbeiter , M. and Patzschke , N. 1996 . Random self-similar multifractals . Math.Nachr. , 181 : 5 – 42 .
  • Cutler , C.D. 1986 . The HausdorfT dimension distribution of finite measures in Euclidian space . Can. J. Math. , 38 : 1459 – 1484 .
  • Dawson , D.A. and Hochberg , K.J. 1979 . The carrying dimension of a stochastic measure diffusion . The Annals of Probability , 7 : 693 – 703 .
  • Falconer , K.J. 1994 . The multifractal spectrum of statistically self-similar measures . J Theor.Prob. , 7 : 681 – 702 .
  • Graf. , S. “ On Bandt's tangential distribution for self-similar measures ” . preprint
  • Hu , X. and Taylor , S.J. 1994 . “ Fractal properties of products and projections of measures in ” . In Math. Proc , Vol. 115 , 527 – 544 . Cambridge Philos. Soc. .
  • Lau , K.S. and Wang , J. 1993 . Mean quadratic variations and Fourier asymptotics of self-similar measures . Mh. Math. , 115 : 99 – 132 .
  • Olsen , L. 1994 . “ Random Geometrically Graph Directed Self-Similar Multifractals ” . Pitman Research Notes in Mathematics Series Vol. 307 ,
  • Patzschke , N. and Zähle , M. 1996 . Self-similar random measures are locally scale invariant . Probab. Th. Rel. Fields , 97 : 559 – 574 .
  • Patzschke , N. and Zähle , U. 1990 . “ Self-similar random measures IV.The recursive construction model of Falconer ” . In Math. Nachr , Vol. 149 , 285 – 302 . Graf, and Mauldin and Williams .
  • Perkins , E.A. 1988 . A space-time property of a class of measure valued branching diffusions . Trans. Amer. Math. Soc. , 305 : 743 – 795 .
  • Rogers , C.A. and Taylor , S.J. 1962 . Functions continuous and singular with respect to a HausdorfT measure . Mathematika , 8 : 1 – 31 .
  • Strichartz , R.S. 1993 . Self-similar measures and their Fourier transforms III . Indiana Univ. Math. J. , 42 : 367 – 411 .
  • Zähle , M. 1996 . Fractal differentiation in the self-similar case . V-Relationships tofractal calculus , 42 appears in Math. Nach.
  • Zähle , U. 1988 . The fractal character of localizable measure valued processes III - Fractal carrying sets of branching diffusions . Math. Nachr. , 138 : 293 – 311 .
  • Zähle , U. 1988 . Self-similar random measures I. Notion, carrying Hausdorff dimension and hyperpolic distribution . Probab. Th. Rel. Fields , 80 : 79 – 100 .
  • Zähle , M. 1995 . The averaged fractal dimension and projections of measures and sets in . Fractals , 3 : 747 – 754 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.