Asymptotics of the quantization errors for condensation measures

Abstract

Let $P:=\frac{1}{3}P\circ S_1^{-1}+\frac{1}{3}P\circ S_2^{-1}+\frac{1}{3}\nu$, where $S_1(x)=\frac{1}{5}x$, $S_2(x)=\frac{1}{5}x+\frac{4}{5}$ for all $x\in \mathbb{R}$, and $\nu$ be a Borel probability measure on $\mathbb{R}$ with compact support. Such a measure $P$ is called a condensation measure, or an an inhomogeneous self-similar measure, associated with the condensation system $(\{S_1, S_2\}, (\frac 13, \frac 13, \frac 13), \gn)$. In this paper, we have explicitly calculated optimal quantizers, quantization dimension, and the lower and upper quantization coefficients for an inhomogeneous self-similar measure.

the result of this paper arXiv:1610.07490 is merged with arXiv:1705.08811

References in corpus (1)

• The local quantization behavior of absolutely continuous probabilities