Communications of the
Korean Mathematical Society CKMS

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, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector 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 $ngeq 2$.

Keywords: Probability measure, infinite iterated function system, optimal set, quantization error

MSC numbers: Primary 60Exx, 28A80, 94A34

Supported by: The research of the second author was supported by U.S. National Security Agency (NSA) Grant H98230-14-1-0320.