Quantization dimension for condensation systems II: The geometric mean error

Quantization Dimension for Random Self-conformal Measures with Respect to the Geometric Error

In this paper, we study the quantization dimension for a random self-conformal measure μ supported on the random self-conformal set E. We establish that the quantization dimension of μ coincides with its Hausdorff dimension with probability one under the strong separation condition.

Quantization Dimension for Conformal Iterated Function Systems

A Note on the Mean - Square Quantization Error

This report summarizes the understanding I have gained in my studies for the independent studies course ENEE 699 up to 15th April, 2000. It includes the derivation of an extension of a result of Wong and Brockett on the behaviour of scalar quantizers. 1 Control under limited communication Let, ẋ(t) = f(x(t), u(t)) + n(t) (1) be a controlled dynamical system where the state x(·) ∈ R, the control...

Quantization Dimension for Infinite Conformal Iterated Function Systems

The quantization dimension function for an F -conformal measure mF generated by an infinite conformal iterated function system satisfying the strong open set condition and by a summable Hölder family of functions is expressed by a simple formula involving the temperature function of the system. The temperature function is commonly used to perform a multifractal analysis, in our context of the m...

Quantization dimension via quantization numbers

We give a characterization of the quantization dimension of Borel probability measures on R in terms of ε-quantization numbers. Using this concept, we show that the upper rate distortion dimension is not greater than the upper quantization dimension of order one. We also prove that the upper quantization dimension of a product measure is not greater than the sum of that of its marginals. Finall...