scholarly journals Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

2013 ◽  
Vol 61 (1) ◽  
pp. 35-45 ◽  
Author(s):  
Mrinal Kanti Roychowdhury
Keyword(s):  
Dimension Estimate ◽  
Quantization Dimension ◽  
Self Similar

scholarly journals The quantization for in-homogeneous self-similar measures with in-homogeneous open set condition

2015 ◽  
Vol 26 (05) ◽  
pp. 1550030 ◽  
Author(s):  
Sanguo Zhu
Keyword(s):  
Open Set Condition ◽  
Similar Measure ◽  
Quantization Dimension ◽  
Open Set ◽  
Quantization Coefficient ◽  
Self Similar ◽  
Quantization Problem

Let [Formula: see text] be a family of contractive similitudes satisfying the open set condition. Let ν be a self-similar measure associated with [Formula: see text]. We study the quantization problem for the in-homogeneous self-similar measure μ associated with a condensation system [Formula: see text]. Assuming a version of in-homogeneous open set condition for this system, we prove the existence of the quantization dimension for μ of order r ∈ (0, ∞) and determine its exact value ξr. The finiteness and positivity of the ξr-dimensional upper and lower quantization coefficient are also explored.

Fractal functional quantization of mean-regular stochastic processes

2010 ◽  
Vol 150 (1) ◽  
pp. 167-191 ◽  
Author(s):  
SIEGFRIED GRAF ◽  
HARALD LUSCHGY ◽  
GILLES PAGÈS
Keyword(s):  
Stochastic Processes ◽  
Probability Measures ◽  
Fractal Measure ◽  
Quantization Dimension ◽  
Regularity Index ◽  
Self Similar ◽  
The Mean ◽  
Functional Quantization ◽  
Borel Probability ◽  
Quantization Problem

AbstractWe investigate the functional quantization problem for stochastic processes with respect toLp(IRd, μ)-norms, where μ is a fractal measure namely, μ is self-similar or a homogeneous Cantor measure. The derived functional quantization upper rate bounds are universal depending only on the mean-regularity index of the process and the quantization dimension of μ and as universal rates they are optimal. Furthermore, for arbitrary Borel probability measures μ we establish a (nonconstructive) link between the quantization errors of μ and the functional quantization errors of the process in the spaceLp(IRd, μ).

Self-similar collapse with non-radial motions

2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  
Self Similar
Sign in / Sign up

Export Citation Format

Share Document