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Some Recent Developments in Quantization of Fractal Measures

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Book cover Fractal Geometry and Stochastics V

Part of the book series: Progress in Probability ((PRPR,volume 70))

Abstract

We give an overview on the quantization problem for fractal measures, including some related results and methods which have been developed in the last decades. Based on the work of Graf and Luschgy, we propose a three-step procedure to estimate the quantization errors. We survey some recent progress, which makes use of this procedure, including the quantization for self-affine measures, Markov-type measures on graph-directed fractals, and product measures on multiscale Moran sets. Several open problems are mentioned.

S. Zhu was supported by China Scholarship Council No. 201308320049

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Author information

Authors and Affiliations

  1. Fachbereich 3 – Mathematik und Informatik, Universität Bremen, Bibliothekstr. 1, Bremen, 28359, Germany

    Marc Kesseböhmer

  2. School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, 213001, China

    Sanguo Zhu

Authors
  1. Marc Kesseböhmer
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  2. Sanguo Zhu
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Corresponding author

Correspondence to Marc Kesseböhmer .

Editor information

Editors and Affiliations

  1. Institut für Mathematik und Informatik, Universität Greifswald, Greifswald, Germany

    Christoph Bandt

  2. Mathematical Institute, University of St Andrews, St Andrews, United Kingdom

    Kenneth Falconer

  3. Institut für Mathematik, Friedrich-Schiller-Universität Jena, Jena, Germany

    Martina Zähle

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Kesseböhmer, M., Zhu, S. (2015). Some Recent Developments in Quantization of Fractal Measures. In: Bandt, C., Falconer, K., Zähle, M. (eds) Fractal Geometry and Stochastics V. Progress in Probability, vol 70. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18660-3_7

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