@mastersthesis {44,
	title = {Construction of optimal quantizers for Gaussian measures on Banach spaces},
	year = {2008},
	school = {Universit{\"a}t Trier},
	abstract = {In this thesis, we investigate the quantization problem of Gaussian measures on Banach spaces by means of constructive methods.
That is, for a random variable $X$ and a natural number $N$, we are searching for those $N$ elements in the underlying Banach space which give the best approximation to $X$ in the average sense.
We particularly focus on centered Gaussians on the space of continuous functions on $[0,1]$ equipped with the supremum-norm, since in that case all known methods failed to achieve the optimal quantization rate for important Gauss-processes.
In fact, by means of Spline-approximations and a scheme based on the Best-Approximations in the sense of the Kolmogorov $n$-width we were able to attain the optimal rate of convergence to zero for these quantization problems.
Moreover, we established a new upper bound for the quantization error, which is based on a very simple criterion, the modulus of smoothness of the covariance function.
Finally, we explicitly constructed those quantizers numerically.},
	keywords = {approximation, Banach space, Brownian motion, Gaussian measures, quantization},
	author = {Benedikt Wilbertz}
}
