Probability distributions supported on sets generated by infinite affine transformations and optimal quantization
Year: 2016
Type: preprint
Abstract: Quantization of a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite set. In this paper, a probability distribution is considered which is generated by an infinite system of affine transformations $S_{ij}$ on $\mathbb R^2$ associated with probabilities $p_{ij}$ such that $p_{ij}>0$ for all $i, j\in \mathbb N$ and $\sum_{i, j=1}^\infty p_{ij}=1$. For such a probability measure $P$, the optimal sets of $n$-means and the $n$th quantization error are calculated for every natural number $n$. In addition, it is shown that the distribution of such a probability measure is same as that of the direct product of the Cantor distribution.
Source: arXiv (Cornell University)
Authors: Doğan Çömez, Mrinal Kanti Roychowdhury
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2340232283