Skip navigation
SuUB logo
DSpace logo

  • Home
  • Institutions
    • University of Bremen
    • City University of Applied Sciences
    • Bremerhaven University of Applied Sciences
  • Sign on to:
    • My Media
    • Receive email
      updates
    • Edit Account details

Citation link: http://nbn-resolving.de/urn:nbn:de:gbv:46-diss000101565
00010156.pdf
OpenAccess
 
copyright

Quantization for probability measures


File Description SizeFormat
00010156.pdf506.17 kBAdobe PDFView/Open
Other Titles: Quantisierung von Wahrscheinlichkeitsmaßen
Authors: Zhu, Sanguo 
Supervisor: Kesseböhmer, Marc
1. Expert: Kesseböhmer, Marc
2. Expert: Graf, Siegfried 
Abstract: 
We introduce the quantization number and the essential covering rate. We treat the quantization for product measures and give effective upper bounds for the quantization dimension of measures. Complete moment condition and limit quantization dimension are introduced and studied.We introduce and study stability and stabilization for dimensions of measures and prove that the stabilized upper quantization dimension coincides with the packing dimension. The quantization for homogeneous Cantor measures are studied in detail to construct examples showing that the lower quantization dimension is not finitely stable.We introduce the upper and lower vanishing rates and study the relationship between the quantization and absolute continuity of measures. We give conditions to ensure monotonicity of the quantization dimension. Measures which are absolutely continuous with respect to self-similar measures are particularly studied.
Keywords: quantization, fractals, stability and stabilisation for dimensions, probability measures
Issue Date: 7-Dec-2005
Type: Dissertation
URN: urn:nbn:de:gbv:46-diss000101565
Institution: Universität Bremen 
Faculty: FB3 Mathematik/Informatik 
Appears in Collections:Dissertationen

  

Page view(s)

42
checked on Feb 25, 2021

Download(s)

10
checked on Feb 25, 2021

Google ScholarTM

Check


Items in Media are protected by copyright, with all rights reserved, unless otherwise indicated.

Legal notice -Feedback -Data privacy
Media - Extension maintained and optimized by Logo 4SCIENCE