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Fractal Geometry and Stochastics II pp 125–146Cite as

Birkhäuser

Random Coverings and Multiplicative Processes

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Part of the book series: Progress in Probability ((PRPR,volume 46))

Abstract

The problems and results on random coverings are described as they arose in the course of history. Then it is explained how the method of multiplicative processes applies in that connection and further examples and generalizations are given.

Multiplicative processes and related martingales appear in a number of circumstances and raise many interesting problems. It would be possible to start with the general theory and show how most problems can be solved in the particular case of random coverings in a very clear manner. We shall go the opposite way. I shall describe the problems and results on random coverings as they arose in the course of history, then explain how the method of multiplicative processes applies in that connection, and go to further examples and generalizations.

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Authors and Affiliations

  1. Mathématiques — Båt. 425, Université de Paris-Sud, 91405, Orsay Cedex, France

    Jean-Pierre Kahane

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  1. Jean-Pierre Kahane
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Editors and Affiliations

  1. Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität, Greifswald, 17487, Germany

    Christoph Bandt

  2. Fakultät für Mathematik und Informatik, Universität Passau, Passau, 94030, Germany

    Siegfried Graf

  3. Mathematisches Institut, Friedrich-Schiller-Universität, Jena, 07740, Germany

    Martina Zähle

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Kahane, JP. (2000). Random Coverings and Multiplicative Processes. In: Bandt, C., Graf, S., Zähle, M. (eds) Fractal Geometry and Stochastics II. Progress in Probability, vol 46. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8380-1_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8380-1_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9542-2

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