Filtern
Erscheinungsjahr
- 2008 (3) (entfernen)
Schlagworte
- Approximation (2)
- Approximationstheorie (1)
- Auslöschung (1)
- Banach space (1)
- Banach-Raum (1)
- Brownian Motion (1)
- Brownsche Bewegung (1)
- Cancellation (1)
- Entire Function (1)
- Error function (1)
- Fehleranalyse (1)
- Fehlerfunktion (1)
- Funktionentheorie (1)
- Gaussian measures (1)
- Gauß-Maß (1)
- Hypergeometrische Funktionen (1)
- Korovkin-Satz (1)
- Mittag-Leffler Funktion (1)
- Mittag-Leffler function (1)
- Polynom-Interpolationsverfahren (1)
- Quantization (1)
- Stochastische Approximation (1)
- Stochastische Quantisierung (1)
- ganze Funktion (1)
- hypergeometric functions (1)
- universal functions (1)
- universelle Funktionen (1)
Institut
- Mathematik (3) (entfernen)
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.