Journal of Theoretical Probability

, Volume 7, Issue 3, pp 681–702

The multifractal spectrum of statistically self-similar measures

  • K. J. Falconer

DOI: 10.1007/BF02213576

Cite this article as:
Falconer, K.J. J Theor Probab (1994) 7: 681. doi:10.1007/BF02213576


We calculate the multifractal spectrum of a random measure constructed using a statistically self-similar process. We show that with probability one there is a multifractal decomposition analogous to that in the deterministic self-similar case, with the exponents given by the solution of an expectation equation.

Key Words

Self-similar process fractals random measure 

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • K. J. Falconer
    • 1
    • 2
  1. 1.School of MathematicsUniversity WalkBristolUK
  2. 2.Mathematical InstituteUniversity of St AndrewsSt AndrewsUK

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