Some Recent Developments in Quantization of Fractal Measures

Part of the Progress in Probability book series (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.

Keywords

Quantization dimension Quantization coefficient Bedford-McMullen carpets Self-affine measures Markov measures Moran measures 

Mathematics Subject Classification (2000).

Primary 28A75 Secondary 28A80 94A15 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Fachbereich 3 – Mathematik und InformatikUniversität BremenBremenGermany
  2. 2.School of Mathematics and PhysicsJiangsu University of TechnologyChangzhouChina

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