QUANTIZATION FOR A PROBABILITY DISTRIBUTION GENERATED BY AN INFINITE ITERATED FUNCTION SYSTEM
Commun. Korean Math. Soc.
Published online May 24, 2022
Lakshmi Roychowdhury and Mrinal Roychowdhury
UTRGV; UTRGV
Abstract : Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, an infinitely generated nonuniform Borel probability measure $P$ is considered on $\mathbb R$. For such a probability measure $P$, an induction formula to determine the optimal sets of $n$-means and the $n$th quantization error for every natural number $n$ is given. In addition, using the induction formula we give some results and observations about the optimal sets of $n$-means for all $n\geq 2$.
Keywords : Nonhomogeneous distribution, infinite iterated function system, optimal set, optimal quantizer, quantization error
MSC numbers : 60Exx, 28A80, 94A34
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