arXiv subjects

Christian Vormoor

Publications and source records attributed to Christian Vormoor.

2 recordsLinked to original sources

arXiv2010

The high resolution vector quantization problem with Orlicz norm distortion

We derive a high-resolution formula for the quantization problem under Orlicz norm distortion. In this setting, the optimal point density solves a variational problem which comprises a function $g:\mathbb{R}_+\to[0,\infty)$ characterizing the quantization complexity of the underlying Orlicz space. Moreover, asymptotically optimal codebooks induce a tight sequence of empirical measures. The set of possible accumulation points is characterized and in most cases it consists of a single element. In that case, we find convergence as in the classical setting.

math.PR↗

arXiv2007

High resolution quantization and entropy coding of jump processes

We study the quantization problem for certain types of jump processes. The probabilities for the number of jumps are assumed to be bounded by Poisson weights. Otherwise, jump positions and increments can be rather generally distributed and correlated. We show in particular that in many cases entropy coding error and quantization error have distinct rates. Finally, we investigate the quantization problem for the special case of $\mathbb{R}^d$-valued compound Poisson processes.

math.PR↗