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Self-similar random measures
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  • Published: December 1988

Self-similar random measures

I. Notion, carrying hausdorff dimension, and hyberbolic distribution

  • U. Zähle1 

Probability Theory and Related Fields volume 80, pages 79–100 (1988)Cite this article

Summary

A set is called self-similar if it is decomposable into parts which are similar to the whole. This notion was generalized to random sets. In the present paper an alternative, axiomatic approach is given which makes precise the following idea (using Palm distribution theory): A random set is statistically self-similar if it is statistically scale invariant with respect to any center chosen at random from that set. For these sets Hausdorff dimension coincides with an intrinsic self-similarity index.

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Authors and Affiliations

  1. Sektion Mathematik, Friedrich-Schiller-Universität, DDR-6900, Jena, German Democratic Republic

    U. Zähle

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  1. U. Zähle
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Zähle, U. Self-similar random measures. Probab. Th. Rel. Fields 80, 79–100 (1988). https://doi.org/10.1007/BF00348753

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  • Received: 16 November 1987

  • Revised: 13 May 1988

  • Issue Date: December 1988

  • DOI: https://doi.org/10.1007/BF00348753

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Keywords

  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Hausdorff Dimension
  • Random Measure
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