Optimal quantization for a probability measure on a nonuniform stretched Sierpi\'{n}ski triangle

Megha Pandey; Mrinal Kanti Roychowdhury

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arXiv · 1606.00963

Optimal quantization for a probability measure on a nonuniform stretched Sierpi\'{n}ski triangle

Megha Pandey·Mrinal Kanti Roychowdhury

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Abstract

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. In this paper, we have considered a Borel probability measure $P$ on $\mathbb R^2$, which has support a nonuniform stretched Sierpi\'{n}ski triangle generated by a set of three contractive similarity mappings on $\mathbb R^2$. For this probability measure, we investigate the optimal sets of $n$-means and the $n$th quantization errors for all positive integers $n$.

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Megha Pandey, Mrinal Kanti Roychowdhury. 2016-06-03. Optimal quantization for a probability measure on a nonuniform stretched Sierpi\'{n}ski triangle. https://arxiv.org/abs/1606.00963

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